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High school mathematics permutation and combination problem-interpolation and insertion.
(1) 3 out of 8 shots and 2 in a row. Problem meaning analysis: 3 discontinuous hits, 2 continuous hits, ***5 hits and 3 misses. There are four gaps before, after and in the three misses, which just add three discontinuous hits and two continuous hits. There are four ways to add * * * C (4,1) = 4; The total number of combinations with 5 out of 8 is 8! /(5! 3! ) = 1 12, so the probability is 4/112 =1/28. (2) spread out the circle and arrange men first. * * * There are six! =720 arrangements, 3 ladies inserted among men, ***6! /3! = 120 arrangements. Note that the leftmost and rightmost sides of a man count as a vacancy, so there are six vacancies among men; So there are 720×120 = 86,400 arrangements.