5 An NSF committee consists of 12 scientists and 8 mathemati

5) An NSF committee consists of 12 scientists and 8 mathematicians. In how many ways can the committee select each of the following :

(a) 3 members to receive first, second, and third place prizes for grant proposals ;

(b) 4 members to attend a conference ;

(c) 2 mathematicians and 2 scientists to attend a conference.

Solution

(a) We need to select 3 members out of a total of 20 members and then arrange them in 3 places. This is done in

C(20,3)*3!=6840

(b) 4 members are selected in:C(20,4)=4845

(c)

This is done in:

C(12,2)C(8,2)=66*28=1848