Lesson Combinations
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Algebra: Combinatorics and Permutations
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Refer to <A HREF=https://www.algebra.com/algebra/homework/Permutations/learning-permutations.lesson?content_action=show_dev>Permutations</A> if you’re not interested in combinations. Combinations are written 3 ways, nCr,C(n,r),and *[illustration choose_function]. <H2>Problem 1</H2> You won a game show and you get to pick 6 out of 13 prizes. How many ways are there to pick any 6? <b>Solution 1</b> There are C(13,6) ways to pick because picking prize A and then prize B is the same as picking prize B and then picking prize A. The formula is {{{nCr=n!/r!(n-r)!}}} So there are {{{13!/6!(13-6)!}}} {{{13!/6!(7!)}}} There are 1716 ways to pick 6 prizes out of 13. <H2>Problem 2</H2> There are 8 letters in a bag. You grab 3 letters. How many combinations are there? <b>Solution 2</b> There are *[illustration combo] ways. {{{8!/3!(8-3)!}}} {{{8!/3!(5!)}}} There are 56 ways.
