Question

a committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 8 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

42042 number of ways can the committee be formed.

Explanation:

Given: There are 8 Faculty member and 15 students eligible to serve on the committee.

Need to form a committee of 4 faculty and 5 students.

Now, finding the number ways that committee to be formed.

lets use the combination formula to find combination of faculty and students.

`_(r)^(n)\textrm{C}= (n!)/(r!(n-r)!)`

Subtituting the value in the formula

⇒
`_(4)^(8)\textrm{C}* _(5)^(15)\textrm{C}= (8!)/(4!(8-4)!) * (15!)/(5!(15-5)!)`

⇒
`_(4)^(8)\textrm{C}* _(5)^(15)\textrm{C}= (8* 7* 6* 5* 4!)/(4!(4)!) * (15* 14* 13* 12* 11* 10!)/(5!(10)!)`

⇒
`_(4)^(8)\textrm{C}* _(5)^(15)\textrm{C}= (8* 7* 6)/(4* 3* 2* 1) * (15* 14* 13* 12* 11)/(5* 4* 3* 2* 1)`

⇒
`_(4)^(8)\textrm{C}* _(5)^(15)\textrm{C}= 14* 3003`

⇒
`_(4)^(8)\textrm{C}* _(5)^(15)\textrm{C}= 42042`

∴ 42042 number of ways can the committee be formed.