2015 Countdown Problem #1: Spelling the New Year
How many ways can the letters of be rearranged such that the first and last letter is the same vowel?
This problem is part of the set 2015 Countdown Problems .
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1 solution
Fix the 2 'E''s on both ends. Thence, you have 11 letters left to arrange, or 11! ways. But, there are 3 T's, 2 N's, and 2 F's. So, we have to divide the product of these to obtain the number of ways: (11!)/(3! 2! 2!)=1663200