// Numbas version: exam_results_page_options
{"name": "Simple Factorial: x!/(y!*z!)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"show_factorial": {"definition": "var out = [];\nfor(var i=n;i>0;i--) {\n  out.push(i);\n}\nvar s = new Numbas.jme.types.TString(out.join(' \\\\times '));\ns.latex = true;\nreturn s;", "type": "string", "parameters": [["n", "number"]], "language": "javascript"}}, "ungrouped_variables": ["a1", "a2", "a3", "b1", "b2", "b3"], "name": "Simple Factorial: x!/(y!*z!)", "tags": [], "advice": "<h4>a)</h4>\n<p>\\[ \\frac{\\var{a1}!}{\\var{a2}! \\times \\var{a3}!}&nbsp;=&nbsp;\\simplify[]{ {fact(a1)}/({fact(a2)}*{fact(a3)})} = \\simplify[fractionnumbers]{{fact(a1)/(fact(a2)*fact(a3))}} \\]</p>\n<h4>b)</h4>\n<p>\\[ \\frac{\\var{b1}!}{\\var{b2}! \\times \\var{b3}!}&nbsp;=&nbsp;\\simplify[]{ {fact(b1)}/({fact(b2)}*{fact(b3)})} = \\simplify[fractionnumbers]{{fact(b1)/(fact(b2)*fact(b3))}} \\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\dfrac{\\var{a1}!}{\\var{a2}!\\times\\var{a3}!}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "fact(a1)/(fact(a2)*fact(a3))", "minValue": "fact(a1)/(fact(a2)*fact(a3))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>$\\dfrac{\\var{b1}!}{\\var{b2}!\\times\\var{b3}!}$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "fact(b1)/(fact(b2)*fact(b3))", "minValue": "fact(b1)/(fact(b2)*fact(b3))", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "<p>Calculate the following factorials.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a1": {"definition": "a2+random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(2..min(a2,5))", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b1": {"definition": "b2+random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(2..min(b2,5))", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}}, "metadata": {"notes": "", "description": "<p>Simplify fractions involving the products of factorials.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Katie Dexter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/553/"}]}]}], "contributors": [{"name": "Katie Dexter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/553/"}]}