SOLUTION: in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class captain has to be included

Algebra ->  Permutations -> SOLUTION: in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class captain has to be included      Log On


   

Question 922183: in how many ways can a group of 5 boys be chosen from a class of twenty boys if the class captain has to be included
Answer by Hawksfan(61) About Me  (Show Source):
You can put this solution on YOUR website!
When order matters, It is a permutation.
If order doesn't matter, It is a combination.
In this case, order DOESNT matter. It is a combination.
n C k = n!/(n-k)!* k!
n is the number of items
k is the number in the subgroup
20 C 5 = 20!/ (20-5)! 5!
(20 *19* 18 *17* 16 * 15!)/15!* 5!
parenthesis don't need to be there but with the computer its hard to
show what numbers are being divided by what.

divide out the 15! to get
20 * 19 * 18 * 17 *16/ 5!
20*19*18*17*16/20*6
5! = 120... now divide by 20
19*18*17*16/6
divide by 6
19*3 *17 * 16 = 15504