Combinations

Combinations can be thought of as a layer on top of permutations. They are employed to solve problems of counting how many selections can be made from a particular group. For example, say I wanted to draw 5 marbles from a bag of 15, how many combinations of marbles could I draw?

To answer this question we have to count how many ways we can draw all 15 marbles and then divide that by the number of ways we can draw 10 marbles. This can be written mathematically as:

n!/(n-r)!

so that is

15! / (15-5)!

=

15! / 10!

=

15*14*13*12*11

= 360,360 ways to draw 5 marbles from the bag of 15.