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
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Permutations
-> 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
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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?
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?
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)
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