Question

How many different committees can be formed from 10 teachers and 49 students if the committee consists of 2 teachers and 4 students?

Answer 1

Given:

Different committees can be formed from 10 teachers and 49 students if the committee consists of 2 teachers and 4 students.

That is;

( 10 choose 2) = C( 10, 2) and ( 49 choose 4) = C(49, 4)

Recall;

`nC_r=(n!)/((n-r)!r!)`

`10C_2=(10!)/((10-2)!2!)=(10*9*8!)/(8!*2!)`

`=5*9=45`

Similarly,

`49C_4=(49!)/((49-4)!4!)=(49!)/(45!*4!)`
`=(49*48*47*46*45!)/(45!*4!)`
`=(49*48*47*46)/(4*3*2*1)`
`=211876`

Now, multiply the two results.

C(10 , 2) x C(49, 4) = 45 x 211876 = 9534420

Hence, it can be form in 9534420 ways.