Question

A club consisting of 6 juniors and 8 seniors is to be formed from a group of 13 juniors and 16 seniors. How many different clubs can be formed from the group?

Answer 1

Answer: 22,084,920 different clubs

Step-by-step explanation:

The club must have 6 juniors and 8 seniors

We have a total of 13 juniors and 16 seniors.

Now, we know that the possible combinations of N objects into a group of K is equal to:

$C = \frac{N!}{(N-K)!*K!}$

For the juniors we have N = 13 and K = 6

$Cj = \frac{13!}{7!*6!} = \frac{13*12*11*10*9*8}{6*5*4*3*2*1} = 1716$

For the seniors we have N = 16 and K = 8

$Cs = \frac{16!}{8!8!} = \frac{16*15*14*13*12*11*10*9}{8*7*6*5*4*3*2*1} = 12870$

Now, as the group consist on both combinations togheter, the number of different clubs that can be formed are:

C = Cj*Cs = 1,716*12,870 = 22,084,920