Download 12.10 Solving Probabilities by Using Combinations A club consists

12.10 Solving Probabilities by Using Combinations
1. A club consists of four men and five women. Three members are to be selected at random to form a committee.
What is the probability that the committee will consist of three women?
2. A flush in the game of poker is five cards of the same suit (5 hearts, 5 diamonds, 5 clubs, or 5 spades). If you are
dealt a five-card hand, determine the probability that you will be dealt a heart flush.
3. A temporary employment agency has six men and five women who wish to be assigned for the day. One
employer has requested four employees for security guard positions, and the second employer has requested
three employees for moving furniture in an office building. If we assume that each of the potential employees
has the same chance of being selected and being assigned at random and that only seven employees will be
assigned, find the probability that
a. Three men will be selected for moving furniture
b. Three men will be selected for moving furniture and four women will be selected for security guard
positions.
4. Conner Shanahan’s rare coin collection is made up of 8 silver dollars, 7 quarters, and 5 dimes. Conner plans to
sell 8 of his 20 coins to finance part of his college education. If he selects the coins at random, what is the
probability that 3 silver dollars, 2 quarters, and 3 dimes are selected?
5. Ten red balls and four blue balls are in a bag. If four balls from the bag are to be selected at random, determine
the probability of selecting four red balls.
6. A dog breeder has 15 puppies for sale, of which 8 are yellow Labrador retrievers. If 5 puppies are selected at
random, determine the probability they are all yellow Labrador retrievers.
7. Each of the digits 0-9 is written on a slip of paper, and the slips are placed in a hat. If three slips of paper are
selected at random, determine the probability that the three numbers selected are greater than 5.
8. Assume that a particular professional baseball team has 10 pitchers, 6 infielders, and 9 other players. If 3
players’ names are selected at random, determine the probability that
a.
b.
c.
d.
All three are infielders
None of the three is a pitcher
2 are pitchers and 1 is an infielder
1 is a pitcher and 2 are players other than pitchers and infielders.