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{"name": "Ioannis's copy of Simple permutation and combination", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "name": "Ioannis's copy of Simple permutation and combination", "variables": {"n": {"group": "Ungrouped variables", "name": "n", "description": "", "definition": "random(4..7)", "templateType": "anything"}, "m": {"group": "Ungrouped variables", "name": "m", "description": "", "definition": "random(4..6)", "templateType": "anything"}, "r": {"group": "Ungrouped variables", "name": "r", "description": "", "definition": "random(2..3)", "templateType": "anything"}}, "parts": [{"customMarkingAlgorithm": "", "scripts": {}, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{n}!", "maxValue": "{n}!", "unitTests": [], "allowFractions": false, "showCorrectAnswer": true, "marks": "4", "prompt": "<p>How many ways are there of arranging $ \\var{n} $ different books on a shelf?</p>"}, {"customMarkingAlgorithm": "", "scripts": {}, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "type": "numberentry", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "correctAnswerFraction": false, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{m}!/({r}! * ({m}-{r})!)", "maxValue": "{m}!/({r}! * ({m}-{r})!)", "unitTests": [], "allowFractions": false, "showCorrectAnswer": true, "marks": "4", "prompt": "<p>How many different ways are there of choosing $\\var{r}$ people from a group of $\\var{m}$ people?</p>"}], "extensions": [], "statement": "<p>Find the number of ways of doing the following.</p>", "preamble": {"css": "", "js": ""}, "advice": "<p>The number of ways of arranging (permuting) a set of $n$ distinct objects is given by $n!$, (said $n$ factorial).</p>\n<p>For instance $5! = 5 \\times 4 \\times 3 \\times 2 \\times 1$.</p>\n<p>When choosing $r$ distinct objects from $n$ (where the order does not matter) the number of different ways of doing this is given by $^nC_r = \\binom{n}{ r}= \\dfrac{n!}{(n-r)! r!}$.</p>\n<p>So for instance the number of ways of choosing 3 objects from 5 will be given by $\\dfrac{5!}{3! \\times 2!} = \\dfrac{ 5 \\times 4}{2 \\times 1} = 10$.</p>\n<p>For more explanation, look for relevant resources in the <a href=\"https://moodle.uel.ac.uk/mod/page/view.php?id=672026\" target=\"_blank\" rel=\"noopener noreferrer\">Maths for Computing</a> section of our <a href=\"https://moodle.uel.ac.uk/course/view.php?id=24176\" target=\"_blank\" rel=\"noopener noreferrer\">Maths Study Skills</a> page.</p>", "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Permutation of n objects; choosing e.g. 3 from 5.</p>"}, "rulesets": {}, "ungrouped_variables": ["n", "m", "r"], "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}]}], "contributors": [{"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}