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1. Arrangements of the letters of TOOT ●○○○○ 10 ptsDetermine the number of distinct ways to arrange the letters of the word TOOT.
2. Orders of breaking clay targets ●●○○○ 20 ptsEight clay targets are arranged in three hanging columns: two columns of three targets each and one column of two targets. A marksman breaks all the targets by these rules: 1. The marksman first chooses a column from which a target is to be broken. 2. The marksman must then break the lowest remaining target in the chosen column. If the rules are followed, in how many different orders can the eight targets be broken?
3. Almost palindromic letter arrangements ●●●○○ 50 ptsCall a string of letters $S$ an almost palindrome if $S$ and the reverse of $S$ differ in exactly two places. Find the number of ways to order the letters in $HMMTTHEMETEAM$ to get an almost palindrome.