// Numbas version: exam_results_page_options
{"name": "Number of multisets from a given set, ", "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(p+b-1,b)", "description": "", "name": "ans"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..10)", "description": "", "name": "p"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(tb<=p,p+1,tb)", "description": "", "name": "b"}, "tb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(7..15)", "description": "", "name": "tb"}}, "ungrouped_variables": ["p", "b", "tb", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Number of multisets from a given set, ", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ans", "minValue": "ans", "correctAnswerFraction": false, "marks": 2, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<p>Number of ways = [[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>A car dealership employs $\\var{p}$ salespeople. A salesperson receives &pound;100 for each car they sell.</p>\n    <p>Yesterday, the dealership sold $\\var{b}$ cars.</p>\n    <p>In how many ways could this happen?</p>\n    <p>(Consider two scenarios different if they result in different bonus payments).</p>", "tags": ["binomial coefficient", "checked2015", "combinations", "combinatorics", "counting", "MAS1701", "MAS2216", "multisets", "sc"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/02/2013:</strong></p>\n        <p>Finished first draft. A description and more tags needed. Included sc tag.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>We are not interested in the order in which the cars were sold, but in the number of cars each salesperson sold.</p>\n    <p>Therefore we are interested in the number of $\\var{b}$-multisets from a set of size $\\var{p}$.</p>\n    <p>So the number of possibilities is given by:</p>\n    <p>\\[\\binom{\\var{p+b-1}}{\\var{b}}=\\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/"}]}