Changes

:<math>\frac {n!}{n_1! n_2! \cdot \cdot \cdot n_r!}</math>, where ''n'' is the total number of objects, and ''n₁'' through ''n_r'' are the total number of each type of objects within the group.

:<math>\frac {n!}{n_1! n_2! \cdot \cdot \cdot n_r!}</math>, where ''n'' is the total number of objects, and ''n₁'' through ''n_r'' are the total number of each type of objects within the group.

For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.

For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 ''p'''s, 2 ''e'''s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.

===Combinations===

===Combinations===

:<math>\begin{pmatrix} n \\ r \end{pmatrix} = \frac{n!}{(n-r)!r!}</math>

:<math>\begin{pmatrix} n \\ r \end{pmatrix} = \frac{n!}{(n-r)!r!}</math>

For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

 

 

==References==

==References==

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[[category: mathematics]]

[[Category:Probability and Statistics]]

[[Category:Mathematics]]