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4 problems match “multinomial coefficients”. Clear

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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. Arranging identical coins ●○○○○ 10 ptsSix identical coins are arranged in a row. Find the number of arrangements in which four are heads and two are tails.
3. 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?
4. Each player gets one ace ●●●○○ 50 ptsA deck of 52 cards containing four aces is shuffled thoroughly and the cards are dealt among four players so that each player receives 13 cards. Find the probability that each player receives exactly one ace. Give the answer as a percentage rounded to one decimal place.