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Magazine Problem 15
Exercises 15-20 involve a deck of 52 cards. If necessary, refer to the picture of a deck of cards, as shown in Figure 11.5 on page 718 . A poker hand consists of five cards. a. Find the total number of possible five-card poker hands. b. A diamond flush is a five-card hand consisting of all diamonds. Find the number of possible diamond flushes. c. Find the probability of being dealt a diamond flush.
Problem 16
Involve computing expected values in games of chance. A game is played using one die. If the die is rolled and shows 1 , the player wins \(\$ 1\); if 2 , the player wins \(\$ 2\); if 3 , the player wins \(\$ 3\). If the die shows 4,5 , or 6 , the player wins nothing. If there is a charge of \(\$ 1.25\) to play the game, what is the game's expected value? What does this value mean?
Problem 17
Evaluate each factorial expression. \(\frac{19 !}{11 !}\)
Problem 17
In the original plan for area codes in 1945, the first digit could be any number from 2 through 9 , the second digit was either 0 or 1 , and the third digit could be any number except 0 . With this plan, how many different area codes are possible?
Problem 18
Evaluate each factorial expression. \(\frac{17 !}{9 !}\)
Problem 19
You draw one card from a 52-card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of drawing a red card each time.
Problem 19
License plates in a particular state display two letters followed by three numbers, such as AT- 887 or BB-013. How many different license plates can be manufactured for this state?
Problem 19
Evaluate each factorial expression. \(\frac{600 !}{599 !}\)
Problem 20
How many different four-letter radio station call letters can be formed if the first letter must be W or K?
Problem 20
You randomly select one card from a 52-card deck. Find the probability of selecting a red 7 or a black 8
