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A chef has 14 brands of hot sauce. In how many ways can the chef pick 3 to mix into a gumbo

User Sanbornc
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Answer:

364ways

Explanation

This is a problem on combination. Combination has to do with selection. For example if r objects are to be selected from a pool of n objects, this can be done in nCr ways.

nCr = n!/(n-r)!r!

If a brand has 14brands of hot sauce and he is to pick 3 to mix into a gumbo, he can select those 3 from a pool of 14brands in 14C3 number of ways.

14C3 = 14!/(14-3)!3!

14C3 = 14!/11!3!

14C3 = 14×13×12×11!/11!×6

14C3 = 14×13×12/6

14C3 = 14×26

14C3 = 364ways

User Gregor Woiwode
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