# There are 10 members in a committee. Out of these 10 members, 6 are women and the remaining members are men. But, now the society has fixed the number of female members to 3 and the number of male members to only 1. In how many ways can this combination be formed which results in a committee of exactly 4 members out of which 3 are female and 1 is men from a total of 10 members

I cannot solve this problem, please help.

*There are 10 members *in* a committee. Out of these 10 members, 6 are women and the remaining members are men. But, now the society has fixed the number of female members to 3 and the number of male members to only 1. In how many ways can this combination be formed which results in a committee of exactly 4 members out of which 3 are female and 1 is men from a total of 10 members*

Thanks.

Your question was –

There are 10 members in a committee. Out of these 10 members, 6 are women and the remaining members are men. But, now the society has fixed the number of female members to 3 and the number of male members to only 1. In how many ways can this combination be formed which results in a committee of exactly 4 members out of which 3 are female and 1 is men from a total of 10 members?

A few days ago I take part an exam where I have faced this GMAT questions and my answers option were –

a. 20

b. 40

c. 60

d. 80

e. None of the above

I have answered as my Correct answer is = d

**Because of this following Explanation:**

According to the question,

**Condition 1:**

Total number of members originally = 10 Total number of female members = 6 Total

number of male members = 4

**Condition 2:**

Total number of members newly = 4 Total number of female members = 3 Total

number of male members = 1

Now, total possible outcomes for 6 females in 3 places = 6*5*4/3*2*1 = 120/6

∴ Total possible outcomes for 6 females in 3 places = 20

Similarly, possible outcomes for 4 males in 1 place = 4/1 = 4.

∴ The total number of combinations is equivalent to the product of the above two results

= 20*4 = 80

**Hence, the correct answer is option d.**

Hope you have got your answer.

Thanks.