Assume that 9 people, including the husband and wife pair, apply 5 sales positio

Question

Assume that 9 people, including the husband and wife pair, apply 5 sales positions. people are hired at random

what is the probability that both the husband and wife are hired?

what is the probability that one is hired and one is not?

Explanation / Answer

a) there are 12 people => 6 pairs we have 5 positions => 1 pairs + 3 can fit now 1 pair can be selected in 6c1 ways now out of remaining 3 there should not be any pairs cases 1) all men => 5c3 ways 2) 2 men 1 woman => 5c2 * 3c1 ways 3)1 man 2 women => 5c1 * 4c2 ways 4)all women => 5c3 ways so total no of ways = 6c1(10+30+30+10)=480 probability = 192/12c5 = 480/95040 b)one hired other not hired. = (6c5 + 6c4 * 2c1 + 6c3 * 3c2 + 6c2 * 4c3 + 6c1 * 5c4 + 6c5) =(6+30+60+60+30+6) =192 probability = 192/95040

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