Lesson Permutations
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Algebra: Combinatorics and Permutations
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This lesson will teach you about permutations. The 2 ways to write permutations are P(n,r) and nPr. The formula is {{{nPr=n!/(n-r)!}}} <H2>Problem 1</H2> How many ways are there for 10 people to finish in top 3? <b>Solution 1</b> There are P(10,3) ways for the 10 people to finish in top 3. {{{10!/(10-3)!}}} {{{10!/7!}}} There are 720 ways. We used permutations because <U>order matters</U>. Combinations are used when order does not matter. <H2>Problem 2</H2> How many ways are there to arrange the words in the word COUNTING? <b>Solution 2</b> There are 8P8 ways. {{{8!/(8-8)!}}} {{{8!/0!}}} There are 40320 ways but we must divide by 2! because there are 2 Ns. So there are 20160 ways.
