College Math

College Math Study Guide

4.13 Chapter Four Review Answers 1. b Solution: This is a problem of combination since the order of selecting is not important. The task is to select 3 males out of 20 males and 2 females out of 10 females. The following formula would be used: C(20, 3) * C(10, 2) = 51,300 2. a Solution: This problem involves the use of both permutation and combination. In selecting the president, head student, and prefix, since the order is vital, it involves the use of permutation. The formula to be used for this selection would be: P (20, 3) = 6840 Now, for selecting the 5 sub prefixes out of the remaining (20- 3) 17 students, combination would be used: C (17, 5) = 6188 The total number of ways will be calculated using the fundamental counting rule, where m = 6840 and n = 6188. Hence, the total number of ways will become: 6840 * 6188 = 42,325,920 3. d Solution: Case I: When two students prefer to stand next to each other, we consider them as one student. So the total number of students become (10- 1) = 9. Moreover, there are two ways in which both can stand. So using permutation (since order is vital), we get the following formula: 2 * P(9,9) = 2* 9! = 725,760 Case II: For this case, the two students do not wish to stand together. The total number of ways all 10 students can be placed is P(10,10) and we have just found that 2*P(9,9) gives the total number of ways in which both stand together. Hence, the total ways in which they both stand apart would be total number of ways less the total number of ways when they both stand together. P( 10, 10) – 2* (9,9) = 3,628,800 – 725,760 = 2,903,040

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