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

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.