RAS question
From 6 men and 4 women, a committee of 3 men and 2 women is to be formed. The number of ways is:
Correct answer: (B) 120.
A committee of 3 men and 2 women chosen from 6 men and 4 women can be formed in 120 ways.
Explanation
This is a combinations question because the committee is selected, not arranged; NCERT states that combinations apply when order is immaterial and gives nCr = n! / r!(n-r)!. Choose the men and women separately, then multiply the choices because both selections are required for one committee. The number of ways to choose 3 men from 6 is C(6,3) = 6! / (3!3!) = 20. The number of ways to choose 2 women from 4 is C(4,2) = 4! / (2!2!) = 6. Therefore, the total number of committees is C(6,3) x C(4,2) = 20 x 6 = 120.
Why the other options are wrong
- (A) 90 is too low because it does not equal the product of the two required independent combinations, C(6,3) and C(4,2).
- (C) 150 is too high because the valid count must be 20 choices for the men multiplied by 6 choices for the women.
- (D) 60 counts only half of the valid product; committee selection ignores order, but it still requires all C(6,3) x C(4,2) possibilities.
Concept
This tests combinations and the multiplication principle in selection problems. RAS reasoning papers often use committee-style questions because they check whether candidates can separate selection from arrangement and combine independent choices correctly.