11.9: Solving Probability Problems by Using Combinations

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Presentation transcript:

11.9: Solving Probability Problems by Using Combinations Example 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? Example 2: You are dealt 5 cards from a standard deck of 52 cards. Determine the probability you are dealt 3 kings and 2 queens.

Example 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 three men will be selected for moving furniture. three men will be selected for moving furniture and four women will be selected for security guard positions.

Example 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? Example 5: 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.