Question

12 women and 18 men are on the faculty in the Computer Science department at Whatsamatta U. a. How many ways are there to select a committee of 6 members of the department if at least two women must be on the committee

Answer 1

183,600 ways

Explanation:

TOPIC : PERMUTATION & COMBINATION

Question: In how many ways can a committee of 6 members - with at least 2 women - be selected?

In other words, how many ways are there, to select a committee of 6 members including at least 2 women?

* Permutation deals with the orderly arrangement of items while Combination deals with the manner of selection of items from a group, without regard to order. In other words, this question has to do with Combination.

There are 12 women and 18 men and you're to select 2 women and 4 men.

The combination for men and women will be found separately and then multiplied together.

WOMEN: 2 OUT OF 12

12! ÷ [2! × (12 - 2)!] = 12! ÷ [2! 10!]

= 12×11×10×9×8×7×6×5×4×3×2×1 = 479,001,600 = 66

2×1 ×10×9×8×7×6×5×4×3×2×1 7,257,600

MEN: 4 OUT OF 18

18! ÷ [4! (18 - 4)!] = 18! ÷ [4! 14!]

= 18×17×16×15×14×13×12×11×10×9×8×7×6×5×4×3×2×1 = 3,060

4×3×2×1 ×14×13×12×11×10×9×8×7×6×5×4×3×2×1

ANSWER:

₁₂C₂ × ₁₈C₄ = 66 × 3060 = 183,600