The board of directors of a large corporation has 12 members

The board of directors of a large corporation has 12 members. In how many ways can one choose the following?

(a) a President, a Vice President, a Treasurer, and a Secretary

(b) any delegation of four memebers?

Solution

(a)

There are 12 members of large corporation

there are 12 way to chose President

hence there are 11 way to chose Vice president

there are 10 way to chose Treasurer

there are 9 way to chose secretary

total no of way to chose = 12 x 11 x 10 x 9 = 11880

(b) we can chose any delegation of four members = nC4

here n= 8 because 4 members are already taken

therefore , we can choose any delegation of four member = 8C4 = 8! /( 4! *4!) = 70