SOLUTION: In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 10 faculty members and 13 students eligible to serve on the c

Question 1089666: In how many ways can a committee consisting of
4
faculty members and
5
students be formed if there are
10
faculty members and
13
students eligible to serve on the committee?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Problem:

In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 10 faculty members and 13 students eligible to serve on the committee?

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Steps:

Use the combination formula to determine how many ways there are to pick the four faculty members (from a pool of ten)
n C r = (n!)/(r!*(n-r)!)
10 C 4 = (10!)/(4!*(10-4)!)
10 C 4 = (10!)/(4!*6!)
10 C 4 = (10*9*8*7*6!)/(4!*6!)
10 C 4 = (10*9*8*7)/(4!)
10 C 4 = (10*9*8*7)/(4*3*2*1)
10 C 4 = 5040/24
10 C 4 = 210
There are 210 different ways to pick the four faculty members (from a pool of ten)

Use the combination formula to determine how many ways there are to pick the five students (from a pool of thirteen)
n C r = (n!)/(r!*(n-r)!)
13 C 5 = (13!)/(5!*(13-5)!)
13 C 5 = (13!)/(5!*8!)
13 C 5 = (13*12*11*10*9*8!)/(5!*8!)
13 C 5 = (13*12*11*10*9)/(5!)
13 C 5 = (13*12*11*10*9)/(5*4*3*2*1)
13 C 5 = 154440/120
13 C 5 = 1287
There are 1287 ways to pick the five students (from a pool of thirteen)

Multiply the two results to get 210*1287 = 270270

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Answer: 270270

Note: it's not a typo that "270" is written twice. Also, the order of any of the members doesn't matter.

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