An NSF committee consists of 12 scientists and 8 mathematici

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.

Please show work Thank you

Solution

(a)

3 can be selected from total 20 in C(20,3) ways and arranged in three places in 3!=6 ways

So total number of ways is:1140*6=6840

(b)

4 can be selected from total 20 in C(20,4) ways

So total number of ways is:4845

(c)

This is done in:C(8,2)C(12,2)=1848