- Intro to Combinations and Permutations
- Permutations with Repetition
- Permutations without Repetition
- Permutations Formula
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License Plates - Android Lock Screen
- Tigers and Bears - Oh My
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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
- 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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