// Numbas version: exam_results_page_options
{"name": "Number of ways of choosing subsets with a condition, ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "m+f", "description": "", "name": "t"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "name": "n"}, "ans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "comb(t,n)-comb(m,n)-comb(f,n)", "description": "", "name": "ans"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "name": "m"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "name": "f"}}, "ungrouped_variables": ["n", "m", "t", "f", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Number of ways of choosing subsets with a condition, ", "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 to form a committee = ?[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>A company has $\\var{t}$ employees, $\\var{m}$ males and $\\var{f}$ females.</p>\n  <p>How many ways are there to form a committee of $\\var{n}$ employees that contains at least one male and one female?</p>", "tags": ["binomial coefficient", "checked2015", "choosing", "choosing subsets", "combinations", "combinatorics", "counting", "MAS1701", "MAS2216", "sc", "selecting"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/02.2013:</strong></p>\n    <p>Finished first draft. Need a description and more tags. Included sc tag.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>There are $\\displaystyle \\binom{\\var{t}}{\\var{n}}$ in which to form the committee when there are no conditions on the number of males and females needed.</p>\n<p>There are $\\displaystyle \\binom{\\var{f}}{\\var{n}}$ ways to form a committee with no males in it.</p>\n<p>There are $\\displaystyle \\binom{\\var{m}}{\\var{n}}$ ways to form a committee with no females in it.</p>\n<p>This give a total of $\\displaystyle \\binom{\\var{t}}{\\var{n}}-\\displaystyle \\binom{\\var{f}}{\\var{n}}-\\displaystyle \\binom{\\var{m}}{\\var{n}}=\\var{ans}$ ways to form the committee with at least one male and one female in it.</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/"}]}