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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