A committee of 5 is to be chosen from a group of 8 men and 4 women. Find the probability that (a

Sarai Davenport

Sarai Davenport

Answered question

2022-06-10

A committee of 5 is to be chosen from a group of 8 men and 4 women.
Find the probability that
(a) the committee consists of 3 men, 2 women;
(b) the first person chosen for the committee is a man, given that the committee must include exactly 2 women;
(c) the first person chosen is a man, given that the last chosen is a woman.

Answer & Explanation

kejohananws

kejohananws

Beginner2022-06-11Added 19 answers

Part (a):
Ways of Selecting:
3 men out of 8: ( 8 3 ) , 2 women out of 4: ( 4 2 ) , 5 people from 12: ( 12 5 )
P (3 men & 2 women) = Favourable Outcomes All Outcomes = ( 8 3 ) × ( 4 2 ) ( 12 5 ) = 336 792
Part (b):
P (Man-first person & Exactly 2 women) = ( 8 3 ) × ( 4 2 ) ( 12 5 ) × 3 × 4 ! 5 ! = 336 792 × 3 5 = 1008 3960
This requires multiplying the two probabilities. Note that the first fraction uses the result from part (a).

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