Question

The judiciary committee at a college is made up of three faculty members and four students. If ten faculty members and 25 students have been nominated for the committee, how many judiciary committees could be formed at this point?

Answer 1

Answer:

1,518,000 committees.

Step-by-step explanation:

We have been given that the  judiciary committee at a college is made up of three faculty members and four students. Ten faculty members and 25 students have been nominated for the committee.

We will use combinations for solve our given problem.

$^nC_r=\frac{n!}{r!(n-r)!}$, where,

n = Number of total items,

r = Items being chosen at a time.

$^{10}C_3\cdot ^{25}C_4=\frac{10!}{3!(10-3)!}\cdot \frac{25!}{4!(25-4)!}$

$^{10}C_3\cdot ^{25}C_4=\frac{10!}{3!*7!}\cdot \frac{25!}{4!*21!}$  

$^{10}C_3\cdot ^{25}C_4=\frac{10*9*8*7!}{3*2*1*7!}\cdot \frac{25*24*23*22*21!}{4*3*2*1*21!}$

$^{10}C_3\cdot ^{25}C_4=10*3*4\cdot 25*23*22$

$^{10}C_3\cdot ^{25}C_4=120\cdot 12650$

$^{10}C_3\cdot ^{25}C_4=1,518,000$

Therefore, 1,518,000 judiciary committees could be formed at this point.