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

i believe the answer is: returns on investments, no wages

people who belong in upper class society would most likely get there by obtaining multiple source of income, which a certain percentage of ownership for businesses. since most of them are job creator, they would most likely get their money from profit, not wages.

money is the anwser i think