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 c

Question

MissTica

2 years ago

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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 c

ommittee must contain four men and four women? if there must be at least tow men? if there must be more women than men?

Social Studies

1 answer:

ddd [48] · Answer 1 · 2022-07-29T00:31:12+03:00

Answer: 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