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 12 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

Answer:

637065

Step-by-step explanation:

12C4 * 13C5= (12*11*10*9)/(4*3*2*1) * (13*12*11*10*9)/(5*4*3*2*1)

Answer 2

Answer: 637065

Step-by-step explanation:

The number of combinations of n things such that m things taken together is given by:-

$C(n;m)=\dfrac{n!}{m!(n-m)!}$

Given : A committee consisting of 4 faculty members and 5 students is to be formed.

There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to firm the committee is formed given by :-

$^{12}C_4\times^{13}C_{5}\\\\=\dfrac{12!}{4!(12-4)!}\times\dfrac{13!}{5!(13-5)!}\\\\=\dfrac{12!}{4!8!}\times\dfrac{13!}{5!8!}\\\\=\dfrac{12\times11\times10\times9\times8!}{24\times8!}\times\dfrac{13\times12\times11\times10\times9\times8!}{120\times8!}\\\\=637065$

Hence, the number of ways to firm the committee is formed = 637065