// Numbas version: finer_feedback_settings
{"name": "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": [{"variable_groups": [], "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "b"}, "ans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "comb(a+b,a)*comb(a+b+c,c)", "description": "", "name": "ans"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "c"}}, "ungrouped_variables": ["a", "c", "b", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Number of permutations of three groups of items, ", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ans", "minValue": "ans", "correctAnswerFraction": false, "marks": 2, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<p>Number of ways = ?[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "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>", "tags": ["checked2015", "combinatorics", "counting", "MAS1701", "MAS2216", "multinomial", "order", "sc", "selection"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/02/2013:</strong></p>\n        <p>Finished first draft. Included sc tag. Need more information for description and for other tags.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>The Multinomial Theorem can be used to count the number of ways.</p>\n    <p>The total number of possibilities = $\\displaystyle \\frac{\\var{a+b+c}!}{\\var{a}!\\var{b}!\\var{c}!}=\\var{ans}$</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}