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7–12 Find the number of distinguishable permutations of the given letters. $$A A B C D$$

Five independent trials of a binomial experiment with probability of success \(p=0.7\) and probability of failure \(q=0.3\) are performed. Find the probability of each event. At most one failure

Find the expected value (or expectation) of the games described.? $$ \begin{array}{l}{\text { A bag contains two silver dollars and eight slugs. You pay }} \\ {50 \text { cents to reach into the bag and take a coin, which you get }} \\ {\text { to keep. }}\end{array} $$

Five independent trials of a binomial experiment with probability of success \(p=0.7\) and probability of failure \(q=0.3\) are performed. Find the probability of each event. At most two failures

Find the expected value (or expectation) of the games described.? $$ \begin{array}{l}{\text { A bag contains eight white balls and two black balls. John }} \\ {\text { picks two balls at random from the bag, and he wins } \$ 5 \text { if he }} \\ {\text { does not pick a black ball. }}\end{array} $$

7–12 Find the number of distinguishable permutations of the given letters. $$A B C D D D E E$$

In how many ways can five different mathematics books be placed next to each other on a shelf?

Five independent trials of a binomial experiment with probability of success \(p=0.7\) and probability of failure \(q=0.3\) are performed. Find the probability of each event. At least two successes

Roulette In the game of roulette as played in Las Vegas, the wheel has 38 slots: Two slots are numbered 0 and 00 , and the rest are numbered 1 to \(36 .\) A \(\$ 1\) bet on any number other than 0 or 00 wins \(\$ 36\) (\$35 plus the \(\$ 1\) bet). Find the expected value of this game.

7–12 Find the number of distinguishable permutations of the given letters. $$X X Y Y Y Z Z Z$$