(a) for each 1≤i≤ n, the i-th tallest boy is not matched with the i-th tallest girl (same sex pairs allowed). (b) Same condition as above, but each pair consists of one person of cach sex
(a) for each 1≤i≤ n, the i-th tallest boy is not matched with the i-th tallest girl (same sex pairs allowed). (b) Same condition as above, but each pair consists of one person of cach sex
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Question
Consider a set of n boys and n girls. No two people have the same height. Use the inclusion-exclusion principle to derive formulas for the number of ways to pair up the 2n people as lab partners that satisfy the following criteria (you can leave the final answer as summations):
(a) for each 1≤i≤ n, the i-th tallest boy is not matched with the i-th tallest girl (same sex pairs allowed).
(b) Same condition as above, but each pair consists of one person of cach sex
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