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Chapter 11: Problem 24
Evaluate each factorial expression. \(6 !-3 !\)
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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?
Five singers are to perform on a weekend evening at a night club. How many different ways are there to schedule their appearances?
Involve computing expected values in games of chance. For many years, organized crime ran a numbers game that is now run legally by many state governments. The player selects a three-digit number from 000 to 999 . There are 1000 such numbers. A bet of \(\$ 1\) is placed on a number, say number 115. If the number is selected, the player wins \(\$ 500\). If any other number is selected, the player wins nothing. Find the expected value for this game and describe what this means.
If a single die is rolled five times, what is the probability it lands on 2 on the first, third, and fourth rolls, but not on either of the other rolls?
A camp counselor and six campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the middle and a camper who has a tendency to engage in food fights must sit to the counselor's immediate left?
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