SOLUTION: In a class of 25, How many ways can a group of five students be selected?

Algebra ->  Permutations -> SOLUTION: In a class of 25, How many ways can a group of five students be selected?      Log On


   

Question 453172: In a class of 25, How many ways can a group of five students be selected?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since order does not matter, we must use the combination formula:


n%21%2F%28n-r%29%21r%21 Start with the given formula



25%21%2F%2825-5%29%215%21 Plug in n=25 and r=5



25%21%2F20%215%21 Subtract 25-5 to get 20


Expand 25!



Expand 20!




Cancel



%2825%2A24%2A23%2A22%2A21%29%2F5%21 Simplify


Expand 5!
%2825%2A24%2A23%2A22%2A21%29%2F%285%2A4%2A3%2A2%2A1%29



6375600%2F%285%2A4%2A3%2A2%2A1%29 Multiply 25*24*23*22*21 to get 6,375,600



6375600%2F120 Multiply 5*4*3*2*1 to get 120



53130 Now divide



So 25 choose 5 (where order doesn't matter) yields 53,130 unique combinations


So there are 53,130 different ways to form a group of 5 people.