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.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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