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

Respuesta :

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  =

  =   [tex]\binom{6}{4}\times\binom{6}{4}[/tex]

 =  [tex]\frac{(6!)}{(2!)(4!)}\times \frac{(6!)}{(2!)(4!)}[/tex] = 225

(2) chose 5 accounting majors  from 6 and chose 3 finance  majors  from 6 =  [tex]\binom{6}{5}\times\binom{6}{3}[/tex]

=  [tex]\frac{(6!)}{(1!)(5!)}\times\frac{(6!)}{(3!)(3!)}[/tex] = 120

=

(3) chose 6 accounting majors  from 6 and chose 2 finance  majors  from 6 = [tex]\binom{6}{6}\times \binom{6}{2}[/tex]

= [tex]\frac{(6!)}{(6!)(0!)}\times\frac{(6!)}{(2!)(4!)}[/tex] = 15

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

                                       = 360

There are 360 ways the fund-raising committee can be formed if at least 4 accounting majors are on the committee

The given parameters are:

Members to select  = 8

Accounting majors = 6

Finance majors = 6

To select at least 4 accounting majors, then the following must be true

(Accounting, Finance) = (4,4) (5,3) (6,2)

So, the number of ways of selecting the committee members is:

[tex]n = ^6C_4 * ^6C_4 + ^6C_5 * ^6C_3 + ^6C_6 * ^6C_2[/tex]

Evaluate the combination expressions

[tex]n = 15 * 15 + 6 * 20 + 1 * 15[/tex]

[tex]n = 360[/tex]

Hence, there are 360 ways the fund-raising committee can be formed if at least 4 accounting majors are on the committee

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