SOLUTION: 5.How many committees of 5 people are possible from a group of 15?

Algebra ->  Permutations -> SOLUTION: 5.How many committees of 5 people are possible from a group of 15?       Log On


   

Question 459810: 5.How many committees of 5 people are possible from a group of 15?

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
The number of ways (or combinations) in which r objects can be selected from a set of n objects, where repetition is not allowed, is denoted by:
.
n C r = %28n%21%29%2F%28r%21%28n-r%29%21%29
.
In your case,
n = number of people in the group = 15
r = number of people in a committee = 5
.
15 C 5 = %2815%21%29%2F%285%21%2815-5%29%21%29+=+%2815%21%29%2F%285%2110%21%29
.
15 C 5 = %2815%2A14%2A13%2A12%2A11%2A10%21%29%2F%285%2A4%2A3%2A2%2A1%2A10%21%29
.
Notice that a bunch of factors will cancel out. Eliminate those before you go to your calculator.
15 C 5 = 7%2A13%2A3%2A11%29
.
15 C 5 = 3003
.
So, there are 3,003 different ways to form 5-person committees from a group of 15 people.

Hope this helps!
Ms. Figge
math_in.the_vortex