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TEAM, MATE, MEAT, AMET, EMAT, TMAE, ...

Twenty-four different “words” can be spelled with the letters in TEAM. We are not requiring them to be real English words, but rather, any and all distinct orderings of the letters. These orderings are called permutations, and the formula for the count of the words using T, E, A and M is 4-factorial, written as 4!

4! = 4 * 3 * 2 * 1 = 24

1. There are only 12 possible “words” using the letters in DEEM. Please explain why, and make an organized list of all 12.

2. List the permutations of the letters in DEED. Explain why there are not as many as for TEAM or DEEM.

3. List the permutations of ABABA. Explain the discrepancy between the count of your list and 5-factorial.

Bonus: Show the “words” you can spell with the letters in DEEDED? Explain the adjustment to 6-factorial needed to count these permutations

Solution

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