There are 10 students (including Alice, Bob, Carol, and Dean) who will be lined up left-to-right according to the following rules: I: Alice must not be rightmost. II: Bob must be adjacent to Carol (either to her right or her left). III: Dean must be placed in the position second from the left. (a) How many possible lineups are there if there are no restrictions? 10! (b) How many possible lineups are there that satisfy I? 10! -9! (c) How many possible lineups are there that satisfy II? 2.9! (d) How many possible lineups are there that satisfy III? 9! (e) How many possible lineups are there that satisfy I and II? (f) How many possible lineups are there that satisfy I and III? (g) How many possible lineups are there that satisfy II and III? (h) How many possible lineups are there that satisfy all three of these rules. (i) How many possible lineups are there that satisfy at least one of these rules.

There are 10 students (including Alice, Bob, Carol, and Dean) who will be lined up left-to-right according to the following rules: I: Alice must not be rightmost. II: Bob must be adjacent to Carol (either to her right or her left). III: Dean must be placed in the position second from the left. (a) How many possible lineups are there if there are no restrictions? 10! (b) How many possible lineups are there that satisfy I? 10! -9! (c) How many possible lineups are there that satisfy II? 2.9! (d) How many possible lineups are there that satisfy III? 9! (e) How many possible lineups are there that satisfy I and II? (f) How many possible lineups are there that satisfy I and III? (g) How many possible lineups are there that satisfy II and III? (h) How many possible lineups are there that satisfy all three of these rules. (i) How many possible lineups are there that satisfy at least one of these rules.

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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