Question

Help!?!? Please??? In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 12 faculty members and 14 students eligible to serve on the committee?

Answer 1

The number of ways is 12C4 + 14C5

Answer 2

they should be multiplied since they are happening simultaneously.

Answer 3

so 12*4 and 14*5?

Answer 4

12!/8!4!*14!/9!5!

Answer 5

@shubhamsrg You are right. Each combination of faculty members can be taken with each combination of students.

Answer 6

^_^
one of the rare achievements for me! :|

Answer 7

@maddiemaze Do you understand how to calculate 12C4 * 14C5 ?

Answer 8

@shubhamsrg Modest hmm..

Answer 9

look who is saying! -_-

Answer 10

no I don't

Answer 11

The method of finding the number of combinations of 12 different things taken 4 at a time comes from the general formula for n things taken r at a time , which is\[nCr=\frac{n!}{(n-r)!r!}\]
\[12C4=\frac{12!}{(12-4)!4!}=\frac{12\times 11\times 10\times 9}{4\times 3\times 2\times 1}\]
Can you try finding 14C5 ?

Answer 12

I think it would be 2002

Answer 13

Correct! Good work. So what do you get when you multiply the two numbers of combinations together?

Answer 14

990990

Answer 15

Absolutely correct! Well done.

Answer 16

Thanks for your help

Answer 17

You're welcome. Sorry for my bad at the start :(