## Quant's probability

danish.hassan7
Good Student
Posts: 10
Joined: Sat Apr 22, 2017 11:51 am

### Quant's probability

What is the logic of the solution of the question given below. I can't understand the given solution

Affirmative action commitments by industrial organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives, which it will fill from among four women and six men. What is the probability that no woman is selected?
a. None of these answers Incorrect
b. 2/15 Incorrect
c. 1/3 Correct
Probability of both positions being filled by men = 6/10*5/9 = 1/3.

edupristine
Finance Junkie
Posts: 873
Joined: Wed Apr 09, 2014 6:28 am

### Re: Quant's probability

Hi Danish,

Explaination:- There are total 10 people for selection (4 women+ 6 Men) choose 2 ways of selecting 2 people for the positions, a combination, which means there are 45 ways(calculated by combination of 10) of selecting 2 people from a pool of 10.

So 45 is in the denominator of the probability.

The probability of no woman selected is 4 women choose 0 multiplied by 6 men choose 2. Again, a combination. 4 women choose 0 equals 1 way. 6 men choose 2 equals 15 ways (6C2) of doing this.

So 1 x 15 = 15. Divide by 45. The probability of selecting 0 women is 15/45, or 1/3, which is about 0.34.

Thanks!