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Chapter 11: Problem 32
Evaluate each factorial expression. \(\frac{17 !}{(17-3) !}\)
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A game is played using one die. If the die is rolled and shows 1 , the player wins \(\$ 5\). If the die shows any number other than 1 , the player wins nothing. If there is a charge of \(\$ 1\) to play the game, what is the game's expected value? What does this value mean?
In Exercises 33-36, we return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting two solid chocolates in a row.
A television programmer is arranging the order in which five movies will be seen between the hours of 6 P.M. and 4 A.M. Two of the movies have a \(G\) rating, and they are to be shown in the first two time blocks. One of the movies is rated NC-17, and it is to be shown in the last of the time blocks, from 2 A.M. until 4 A.M. Given these restrictions, in how many ways can the five movies be arranged during the indicated time blocks?
Consider a political discussion group consisting of 5 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Republican.
You need to arrange ten of your favorite photographs on the mantel above a fireplace. How many ways can you arrange the photographs, assuming that the order of the pictures makes a difference to you?
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