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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 42e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 42e

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# A starting lineup in basketball consists of two guards,

ISBN: 9780321629111 32

## Solution for problem 42E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 42E

A starting lineup in basketball consists of two guards, two forwards, and a center. a. ?A certain college team has on its roster three centers, four guards, four forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [?Hint?: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] b. ?Now suppose the roster has 5 guards, 5 forwards, 3 centers, and 2 “swing players” (X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup?

Step-by-Step Solution:

Answer Step 1 of 2 a) There are three possibilities: x is not picked, x is picked as a forward, and x is picked as a guard. When x is not picked Number of different lineups= (4 2)(4 2)(3 1)=108 c c c when x is picked as a forward, you only need to pick one more forward, Number of different lineups= (4 1)(4 2)c 1)c2 c the same number will result when you pick x as a guard: 72 By adding all three results number of lineups=108+72+72=252

Step 2 of 2

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