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We can choose from *20* people. This is n.<\/p>\n\n

We are choosing *4* people. This is r.<\/p>\n"]},"subContentId":"3086a880-1d13-4d43-b44e-b84e20de147c","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"n and r"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":64.41048034934498,"y":27.184466019417474,"width":13.537117903930131,"height":9.606986899563319,"duration":{"from":220.772,"to":220.772},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"Fill in the missing words","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","submitAnswer":"Submit","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again.","a11yCheckingModeHeader":"Checking mode","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

20P4 = 20!\/(20-4)!
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20x19x18x17 = *116280 \/ 116 280 \/ 116,280*<\/p>\n"]},"subContentId":"abe07c37-090b-430d-aa28-8e7517356369","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"answer"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":1.0917030567685588,"y":21.35922330097087,"width":13.537117903930131,"height":10,"duration":{"from":303.988,"to":303.988},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"Fill in the missing words","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","submitAnswer":"Submit","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again.","a11yCheckingModeHeader":"Checking mode","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

20P4 = 20!\/16!
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Look for the permutations button on your calculator and verify that you do still get 20P4 = 116 280.<\/p>\n\n

*** note that NOT ALL calculators have this button, but most do<\/p>\n"},"subContentId":"aab4aa0f-0b02-4429-bb8b-c617a7776f96","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"visuals":{"backgroundColor":"rgb(255, 255, 255)","boxShadow":true},"goto":{"url":{"protocol":"http:\/\/"},"visualize":false,"type":""},"label":""},{"x":1.0917030567685588,"y":85.43689320388349,"width":23.144104803493452,"height":3.056768558951965,"duration":{"from":422.307,"to":422.307},"libraryTitle":"Text","action":{"library":"H5P.Text 1.1","params":{"text":"

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What does this new formula for combinations look similar to?<\/p>\n","answers":["

permutations formula<\/p>\n","

factorials<\/p>\n","

Pythagorean Theorem<\/p>\n","

Nothing, it's all gibberish<\/p>\n"]},{"subContentId":"1e4c3372-2afc-49be-a87e-106f921ff441"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"autoContinue":true,"timeoutCorrect":2000,"timeoutWrong":3000,"soundEffectsEnabled":true,"enableRetry":true,"enableSolutionsButton":true,"passPercentage":100},"l10n":{"nextButtonLabel":"Next question","showSolutionButtonLabel":"Show solution","retryButtonLabel":"Retry","solutionViewTitle":"Solution list","correctText":"Correct!","incorrectText":"Incorrect!","muteButtonLabel":"Mute feedback sound","closeButtonLabel":"Close","slideOfTotal":"Slide :num of :total","scoreBarLabel":"You got :num out of :total points","solutionListQuestionNumber":"Question :num","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again."}},"subContentId":"082266a8-d1b8-4371-b4d6-a1e3a5584cbf","metadata":{"contentType":"Single Choice Set","license":"U","title":"similar to"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":33.842794759825324,"y":52.42718446601941,"width":25.589519650655024,"height":9.830103711790393,"duration":{"from":549.735,"to":549.735},"libraryTitle":"Single Choice Set","action":{"library":"H5P.SingleChoiceSet 1.11","params":{"choices":[{"subContentId":"7bba9ea7-a415-4977-868d-90088420f2fc","question":"

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No, so we use combinations.<\/p>\n","

Yes, so we use permutations.<\/p>\n"]},{"subContentId":"a5abe349-4704-4914-8b41-21c6589831f6"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"autoContinue":true,"timeoutCorrect":2000,"timeoutWrong":3000,"soundEffectsEnabled":true,"enableRetry":true,"enableSolutionsButton":true,"passPercentage":100},"l10n":{"nextButtonLabel":"Next question","showSolutionButtonLabel":"Show solution","retryButtonLabel":"Retry","solutionViewTitle":"Solution list","correctText":"Correct!","incorrectText":"Incorrect!","muteButtonLabel":"Mute feedback sound","closeButtonLabel":"Close","slideOfTotal":"Slide :num of :total","scoreBarLabel":"You got :num out of :total points","solutionListQuestionNumber":"Question :num","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again."}},"subContentId":"03c2cbff-4264-411d-92a5-4c419c9e26f1","metadata":{"contentType":"Single Choice Set","license":"U","title":"order"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":60.043668122270745,"y":54.36893203883495,"width":13.973799126637555,"height":8.733624454148472,"duration":{"from":562.765,"to":562.765},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"

Fill in the blanks<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","submitAnswer":"Submit","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again.","a11yCheckingModeHeader":"Checking mode","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

*23*C*6*<\/p>\n"]},"subContentId":"21258400-be6f-4614-87da-534e4d947a39","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"n and r"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":62.22707423580786,"y":40.77669902912621,"width":14.41048034934498,"height":10,"duration":{"from":673.35,"to":673.35},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"Fill in the missing words","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","submitAnswer":"Submit","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again.","a11yCheckingModeHeader":"Checking mode","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

23C6 = 23x11x21x19
\n= *100 947 \/ 100947 \/ 100,947*<\/p>\n"]},"subContentId":"2b918630-b51e-424b-985e-59c8eae0d719","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"answer"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":0,"y":36.89320388349514,"width":13.537117903930131,"height":10,"duration":{"from":719.149,"to":719.149},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"Fill in the missing words","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","submitAnswer":"Submit","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","a11yCheck":"Check the answers. The responses will be marked as correct, incorrect, or unanswered.","a11yShowSolution":"Show the solution. The task will be marked with its correct solution.","a11yRetry":"Retry the task. Reset all responses and start the task over again.","a11yCheckingModeHeader":"Checking mode","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

23C6 = 23!\/(17!6!)
\n= *100 947 \/ 100947 \/ 100,947*<\/p>\n"]},"subContentId":"e347fc9b-f06d-438f-90b3-c16e49dcf937","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"answer"}},"pause":true,"displayType":"poster","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":0,"y":69.86899563318778,"width":7.860262008733625,"height":6.774017467248909,"duration":{"from":754.096,"to":763},"libraryTitle":"Text","action":{"library":"H5P.Text 1.1","params":{"text":"

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5b. Principles of Counting - perms and combs

Michelle Ripley