An 8-person committee is to be formed from a group of 15 women and 12 men. In how many ways can the committee be formed if the committee must contain four men and four women? if there must be at least tow men? if there must be more women than men?

675675; 2136420; 1068210

Explanation:

THE problem can be approached using the combination technique,which determines the number of possible arrangement in a collective without credence to the order of arrangement.

Number of women = 15

Nunber of men = 12

Total committee members = 8

nCr = n! ÷ (n-r)!r!

QUESTION 1

Committee must contain 4men and 4women

12C4×15C4 = 12!÷(12-4)!4! × 15!÷(15-4)!4!

(12! ÷ 8!4!) × (15! ÷ 11!4!)

(11880 ÷ 24) × (32760 ÷ 24)

495 × 1365 = 675675ways

QUESTION 2

If there must be atleast two men

Possible combination ;

12C8×15C0 + 12C7×15C1 + 12C6×15C2 + 12C5×15C3 + 12C4×15C4 + 12C3×15C5 + 12C2×15C6 =2136420ways

QUESTION 3

If there must be more women than men

Possible combination;

12C1×15C7 + 12C2×15C6 + 12C3×15C5 = 1068210 ways

because the early people found out about it.