A, B, C, D, and E are deciding the order of tryouts.(a) B does not want to be the ﬁrst and D does not want to be the last. How many orders are possible?(b) If C and E do not want to go consecutively, how many orders are possible?(c) If A and B want to go consecutively. How many orders are possible?(d) What is the probability that A and B are presenting consecutively if the order is randomly generated?

Answered: A, B, C, D, and E are deciding the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A, B, C, D, and E are deciding the order of tryouts.

(a) B does not want to be the ﬁrst and D does not want to be the last. How many orders are possible?

(b) If C and E do not want to go consecutively, how many orders are possible?

(d) What is the probability that A and B are presenting consecutively if the order is randomly generated?

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Given
A, B, C, D, E are deciding the order of tryouts.

a)
The total number of ways of ordering five persons A, B, C, D, E $= 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$
The number of ways where B is the first to order $= 1 \times 4! = 24$
The number of ways where D is the last to order $= 4! \times 1 = 24$
The number of ways where B is the first and D is the last to order $= 1 \times 3! \times 1 = 6$

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