 Intro to Combinations and Permutations
 Permutations with Repetition
 Permutations without Repetition
 Permutations Formula

License Plates  Android Lock Screen
 Tigers and Bears  Oh My

Combination without Repetition  Combination Formula
 Combining Combinations

The String of Beads  Anagrams
 Combinations with Repetition I
 Combinations with Repetition II
Combination Formula
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To calculate the number of possible combinations of r elements from n elements, you can do the following:
 Calculate (n Permute r)
 Divide nPr by r!, the number of permutations of r itself. This is because there will be r! permutations for each combination.
The Combination formula can be expressed as one formula. Recall the permutation formula:
n!
You can then just divide by r! to get the Combination formula:
The number of ways you can choose *r* elements from *n* elements =
nCr =
The # of ways to permute *r* elements from *n* elements รท by r!, the # of permutations for each combination of *r* elements.
n!
This formula can be shortened to:
(n choose r)
on a calculating device, though again there may be cases where the formula does not apply.
Challenge
In the powerball lottery, 5 balls are chosen from 59 different white balls and 1 ball is chosen from 35 different red balls. The order they are chosen in does not matter. How many outcomes are possible?
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