// Numbas version: finer_feedback_settings
{"name": "Number of combinations without replacement - lotto ticket, ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(4..7)", "description": "", "name": "b"}, "ans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "comb(a,b)", "description": "", "name": "ans"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(30..50)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "b", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Number of combinations without replacement - lotto ticket, ", "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 tickets = ?[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>In a lotto game a player buys a ticket and selects $\\var{b}$ numbers from a list of the numbers from $1$ to $\\var{a}$.</p>\n  <p>Then $\\var{b}$ winning numbers are selected at random without replacement.</p>\n  <p>How many tickets would you need to buy in order to be sure of choosing all $\\var{b}$ numbers correctly?</p>", "tags": ["binomial coefficients", "checked2015", "choosing without replacement", "combinations", "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. Description and tags need to be completed. Added tag sc.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>Each choice of $\\var{b}$ numbers results in a subset of the numbers $1$ to $\\var{a}$.</p>\n  <p>The number of such possibilities is equal to the number of $\\var{b}$-subsets of $\\var{a}$ elements, so you need to buy this number of tickets to guarantee a win!</p>\n  <p>\\[\\binom{\\var{a}}{\\var{b}}=\\var{ans}.\\]&nbsp;</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/"}]}