// Numbas version: exam_results_page_options
{"name": "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": [{"variable_groups": [], "variables": {"ans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "comb(n,a)*comb(n-a,b)*comb(n-a-b,c)*comb(d+f,d)", "description": "", "name": "ans"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a+b+c+d+f", "description": "", "name": "n"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..3)", "description": "", "name": "c"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "name": "f"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "d"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "c", "b", "d", "f", "n", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Coefficient in the expansion of a multinomial, ", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ans", "minValue": "ans", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<p>Coefficient = ?[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "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": ["checked2015", "coefficients in an expansion", "combinatorics", "MAS1701", "MAS2216", "multinomial coefficient", "multinomial theorem"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/02/2013:</strong></p>\n    <p>Finished first draft. Need a description and perhaps more tags.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "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/"}]}