Question

A business organization needs to make up a 8 member fund-raising committee. The organization has 6 accounting majors and 6 finance majors. In how many ways can the fund-raising committee be formed if at least 4 accounting majors are on the committee

Answer 1

Answer:

Total no of ways can the fund raising committee be formed if at least 4 accounting majors are on the committee. = 360

Step-by-step explanation:

Given  -  

A business organization needs to make up a 8 member fund-raising committee.

The organization has 6 accounting majors and 6 finance majors .

Total no of ways can the fund raising committee be formed if at least 4 accounting majors are on the committee.

(1) chose 4 accounting majors  from 6 and chose 4 finance  majors  from 6  =

  =   $\binom{6}{4}\times\binom{6}{4}$

 =  $\frac{(6!)}{(2!)(4!)}\times \frac{(6!)}{(2!)(4!)}$ = 225

(2) chose 5 accounting majors  from 6 and chose 3 finance  majors  from 6 =  $\binom{6}{5}\times\binom{6}{3}$

=  $\frac{(6!)}{(1!)(5!)}\times\frac{(6!)}{(3!)(3!)}$ = 120

=

(3) chose 6 accounting majors  from 6 and chose 2 finance  majors  from 6 = $\binom{6}{6}\times \binom{6}{2}$

= $\frac{(6!)}{(6!)(0!)}\times\frac{(6!)}{(2!)(4!)}$ = 15

Then total no of ways = (1) + (2) + 3

                                       = 360