Question

The Delta Secret Philosophy society has just recruited three football players, two nerds, and fourcomputer geeks. Big Nico picks four of these new members at random for the philosophical discussion team.

(a) How many different sets of four new members are possible?
(b) How many of those sets of 4 contain both nerds and two computer geeks?

Answer 1

126,168

Explanation:

Given that the Delta Secret Philosophy society has just recruited three football players, two nerds, and fourcomputer geeks. Big Nico picks four of these new members at random for the philosophical discussion team.

a) Out of 9 persons 4 new members can be selected at random in

9C4 ways

= 126

b) There shouldbe atleast one nerd and one computer geek for this

i.e. for the four, 1 nerd and one geek should be compulsorily selected with remaining 2 randomly from the remains 7 persons

One nerd can be selected from 2 nerds in 2 ways

One geek can be selected from 4 geeks in 4 ways

Remaining 2 can be selected frm remaining 7 in 7C2 ways

So no of ways=
`2*4*7C2\\= 8 * 21\\=168`

168 ways