a. Find the total number of possible 4-member committees. b. Find the number of

Question

a. Find the total number of possible 4-member committees. b. Find the number of possible 4-member committees that only contain girls. c. Find the probability that a 4-member committee chosen at random will only contain girls. d. Find the probability that a 4-member committee chosen at random will contain at least one girl. Lesson 9-5 Using Permutations and Combinations in Probability d 1. Ten people are to be seated on 10 chairs in a line. Among them is a family of 3 that does not want to be separated. How many different seating arrangements are possible? Explain how you arrived at your answer. 2. There are four basic types of problems in this lesson. Explain the similarities and differences between them. 3. In a class of 10 boys and 12 girls, four students are to be chosen to serve on a committee. Find the total number of possible 4-member committees. Find the number of possible 4-member committees that only contain girls. Find the probability that a 4-member committee chosen at random will only contain girls. Find the probability that a 4-member committee chosen at random will contain at least one girl. a. b. c. d. 4. Three men and four women stand in line at a checkout counter at a store. In how many ways can they stand in the line if we consider only their gender? 5. Classify each of the following as true or false. If false, demonstrate why. 6! 6! 5! 6! c. _=15

Explanation / Answer

In a class of 10 boys and 12 girls, four students are to be chosen to serve on a committee.

a. The total number of possible 4-member committees = Choose four out of 22 students = 22C4 = 7315

b. The number of possible 4-member committees that only contain girls = 12C4 = 495

c. The probability that a 4-member committee chosen at random will only contain girls = 12C4/22C4 = 495/7315 = 0.0676

d. .

Number of possible 4-member committees contain at least one girl = Total possible committees - Number of committees with no girls = 7315 - 10C4 = 7105

The probability that a 4-member committee chosen at random will contain at least one girl = 7105/7315 =0.9712

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