// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Number of permutations of three groups of items,", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variable_groups": [], "statement": "<p>Suppose I drink $\\var{a}$ cups of water, $\\var{b}$ cups of tea, and $\\var{c}$ cups of coffee every day. How many ways can I arrange the order in which I drink them?</p>", "name": "Simon's copy of Number of permutations of three groups of items,", "preamble": {"js": "", "css": ""}, "functions": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "ungrouped_variables": ["a", "c", "b", "ans"], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "type": "gapfill", "marks": 0, "scripts": {}, "customName": "", "prompt": "<p>Number of ways = ?[[0]]</p>", "sortAnswers": false, "useCustomName": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "type": "numberentry", "marks": 2, "allowFractions": false, "scripts": {}, "correctAnswerFraction": false, "customName": "", "maxValue": "ans", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "mustBeReduced": false, "useCustomName": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "minValue": "ans", "showFractionHint": true}]}], "tags": [], "variables": {"a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "a"}, "c": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "c"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..5)", "name": "b"}, "ans": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "comb(a+b,a)*comb(a+b+c,c)", "name": "ans"}}, "advice": "<p>The total number of ways can be counted using the Multinomial Theorem:</p>\n<p></p>\n<p>$ {\\var{a+b+c}} \\choose {\\var{a},\\var{b},\\var{c}}$$ =&nbsp; \\frac{\\var{a+b+c}!}{\\var{a}!\\var{b}!\\var{c}!}=\\var{ans}$</p>", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}