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\\[ \\frac{\\var{a1}!}{\\var{a2}! \\times \\var{a3}!} = \\simplify[]{ {fact(a1)}/({fact(a2)}*{fact(a3)})} = \\simplify[fractionnumbers]{{fact(a1)/(fact(a2)*fact(a3))}} \\]
\n\\[ \\frac{\\var{b1}!}{\\var{b2}! \\times \\var{b3}!} = \\simplify[]{ {fact(b1)}/({fact(b2)}*{fact(b3)})} = \\simplify[fractionnumbers]{{fact(b1)/(fact(b2)*fact(b3))}} \\]
", "functions": {"show_factorial": {"type": "string", "parameters": [["n", "number"]], "language": "javascript", "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;"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "a3", "b1", "b2", "b3"], "showQuestionGroupNames": false, "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "rulesets": {}, "metadata": {"description": "Simplify fractions involving the products of factorials.
", "licence": "Creative Commons Attribution 4.0 International", "notes": ""}, "statement": "Calculate the following factorials.
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", "showPrecisionHint": false, "maxValue": "fact(b1)/(fact(b2)*fact(b3))", "minValue": "fact(b1)/(fact(b2)*fact(b3))"}], "name": "Marlon's copy of Simple Factorial: x!/(y!*z!)", "preamble": {"js": "", "css": ""}, "variables": {"a3": {"name": "a3", "group": "Ungrouped variables", "definition": "random(2..min(a2,5))", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "a2+random(3..5)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "b2+random(2..5)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(2..15)", "description": "", "templateType": "anything"}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "random(2..min(b2,5))", "description": "", "templateType": "anything"}}, "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}