How many ways can the letters of $\boxed{TWENTY FIFTEEN}$ be rearranged such that the first and last letter is the same vowel?

*
This problem is part of the set
2015 Countdown Problems
.
*

1663200
2015200
3243200
9979200

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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