Home / Assignment Help / URGENT A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women? A. 5/143 B. 7/143 C. 28/143 D. 30/143

URGENT A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women? A. 5/143 B. 7/143 C. 28/143 D. 30/143

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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