Counting: permutations and combinations Test

{"questions":[{"content":"Choose a chair, secretary and treasurer from eight people, with no shared roles. How many assignments? [[input-counting-test-1]]","widgets":{"input-counting-test-1":{"type":"input","answer":"336"}},"hints":[],"explanation":"Distinct roles give 8 choices, then 7, then 6: 8 × 7 × 6 = 336.","id":"counting-test-1","coverage_topics":["aa-hl-permutations"],"correct_feedback":"Distinct roles give 8 choices, then 7, then 6: 8 × 7 × 6 = 336.","incorrect_feedback":"Distinct roles give 8 choices, then 7, then 6: 8 × 7 × 6 = 336.","evidence_kind":"objective-concept-test"},{"content":"A display uses four of seven distinct exhibits, with one of the four labelled as the featured exhibit. How many displays are possible? [[input-counting-test-2]]","widgets":{"input-counting-test-2":{"type":"input","answer":"140"}},"hints":[],"explanation":"Choose the four exhibits in C(7,4) = 35 ways, then choose the featured one in 4 ways.","id":"counting-test-2","coverage_topics":["aa-hl-combinations"],"correct_feedback":"Choose the four exhibits in C(7,4) = 35 ways, then choose the featured one in 4 ways.","incorrect_feedback":"Separate selecting the group from assigning the one distinguished role.","evidence_kind":"objective-concept-test"},{"content":"How many length-five strings use only P and Q and contain at least one Q? [[input-counting-test-3]]","widgets":{"input-counting-test-3":{"type":"input","answer":"31"}},"hints":[],"explanation":"There are 2⁵ = 32 strings in total. Only PPPPP has no Q, so subtract 1.","id":"counting-test-3","coverage_topics":["aa-hl-permutations"],"correct_feedback":"There are 2⁵ = 32 strings in total. Only PPPPP has no Q, so subtract 1.","incorrect_feedback":"Count every string, then remove the strings that fail the at-least-one condition.","evidence_kind":"objective-concept-test"},{"content":"How many four-digit integers use 0,1,2,3 without repetition? [[input-counting-test-4]]","widgets":{"input-counting-test-4":{"type":"input","answer":"18"}},"hints":[],"explanation":"The first digit has three nonzero choices, then the remaining digits have 3! orders.","id":"counting-test-4","coverage_topics":["aa-hl-permutations"],"correct_feedback":"The first digit has three nonzero choices, then the remaining digits have 3! orders.","incorrect_feedback":"The first digit has three nonzero choices, then the remaining digits have 3! orders.","evidence_kind":"objective-concept-test"},{"content":"Choose three from nine people, including two specified people. How many groups? [[input-counting-test-5]]","widgets":{"input-counting-test-5":{"type":"input","answer":"7"}},"hints":[],"explanation":"Only one place remains, chosen from the seven others.","id":"counting-test-5","coverage_topics":["aa-hl-combinations"],"correct_feedback":"Only one place remains, chosen from the seven others.","incorrect_feedback":"Only one place remains, chosen from the seven others.","evidence_kind":"objective-concept-test"},{"content":"A team of three is chosen from four juniors and five seniors, with at least one junior. How many teams? [[input-counting-test-6]]","widgets":{"input-counting-test-6":{"type":"input","answer":"74"}},"hints":[],"explanation":"C(9,3) − C(5,3) = 84 − 10 = 74.","id":"counting-test-6","coverage_topics":["aa-hl-combinations"],"correct_feedback":"C(9,3) − C(5,3) = 84 − 10 = 74.","incorrect_feedback":"C(9,3) − C(5,3) = 84 − 10 = 74.","evidence_kind":"objective-concept-test"},{"content":"Six distinct books are arranged on a shelf. Two specified books must be adjacent. How many orders? [[input-counting-test-7]]","widgets":{"input-counting-test-7":{"type":"input","answer":"240"}},"hints":[],"explanation":"Treat the pair as a block: 5! orders, with two internal orders, giving 240.","id":"counting-test-7","coverage_topics":["aa-hl-permutations"],"correct_feedback":"Treat the pair as a block: 5! orders, with two internal orders, giving 240.","incorrect_feedback":"Treat the pair as a block: 5! orders, with two internal orders, giving 240.","evidence_kind":"objective-concept-test"},{"content":"Select two red and two blue counters from five distinct red and six distinct blue counters. How many selections? [[input-counting-test-8]]","widgets":{"input-counting-test-8":{"type":"input","answer":"150"}},"hints":[],"explanation":"C(5,2)C(6,2) = 10 × 15 = 150.","id":"counting-test-8","coverage_topics":["aa-hl-combinations"],"correct_feedback":"C(5,2)C(6,2) = 10 × 15 = 150.","incorrect_feedback":"C(5,2)C(6,2) = 10 × 15 = 150.","evidence_kind":"objective-concept-test"}],"mix":0,"tinkumo_module_mode":"test"}