// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Coefficient in the expansion of a multinomial,", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variable_groups": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"marks": 0, "showCorrectAnswer": true, "customName": "", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "unitTests": [], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "prompt": "<p>Coefficient = ?[[0]]</p>", "variableReplacements": [], "customMarkingAlgorithm": "", "useCustomName": false, "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "customName": "", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "type": "numberentry", "unitTests": [], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "mustBeReducedPC": 0, "variableReplacements": [], "allowFractions": false, "customMarkingAlgorithm": "", "useCustomName": false, "scripts": {}, "maxValue": "ans", "showFractionHint": true, "minValue": "ans", "showFeedbackIcon": true}], "showFeedbackIcon": true}], "variablesTest": {"condition": "n<=15", "maxRuns": 100}, "name": "Simon's copy of Coefficient in the expansion of a multinomial,", "variables": {"d": {"description": "", "definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "d"}, "a": {"description": "", "definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a"}, "ans": {"description": "", "definition": "comb(n,a)*comb(n-a,b)*comb(n-a-b,c)*comb(d+f,d)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans"}, "n": {"description": "", "definition": "a+b+c+d+f", "templateType": "anything", "group": "Ungrouped variables", "name": "n"}, "c": {"description": "", "definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c"}, "f": {"description": "", "definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "f"}, "b": {"description": "", "definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b"}}, "preamble": {"css": "", "js": ""}, "advice": "<p>The Multinomial Theorem can be used to solve this question.</p>\n  <p>The coefficient is:&nbsp;</p>\n  <p>\\[\\frac{\\var{n}!}{\\var{a}!\\var{b}!\\var{c}!\\var{d}!\\var{f}!}=\\var{ans}\\]</p>", "ungrouped_variables": ["a", "c", "b", "d", "f", "n", "ans"], "rulesets": {}, "statement": "<p>What is the coefficient of $x_1^{\\var{a}}x_2^{\\var{b}}x_3^{\\var{c}}x_4^{\\var{d}}x_5^{\\var{f}}$ in the expansion of $(x_1+x_2+x_3+x_4+x_5)^{\\var{n}}$?</p>", "tags": [], "extensions": [], "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/"}]}