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Consider the word: MATH. You want to take three letters from this word and rearrange them. ( 30 points total) a) Is this a permutation problem or a combination problem? Explain. (6 points) b) Set up a formula using either

`_(n)P_(r)`

or

`_(n)C_(r)`

to solve this problem. (6 points) c) How many ways can you select three letters from MATH and rearrange them? (6 points) d) If you randomly rearrange three letters from MATH, what is the probability of the letter "

`A`

" being the first one? ( 6 points) e) Consider another word: POTATO. How many ways can you rearrange the letters of this word? (6 points)