a) In how many ways can 6 people be seated in a row of 12 sests so that here are no unoccupied seats between people. b) In how many ways can the 9 US supreme court justices be seated for a photo-session so that none the three women justices sit side by side? c) In a pack of 100 light bulbs, 10 are defective. Samples of 5 bulbs are selected randomly. How many samples conatain at least one defective bulb?

a) In how many ways can 6 people be seated in a row of 12 sests so that here are no unoccupied seats between people. b) In how many ways can the 9 US supreme court justices be seated for a photo-session so that none the three women justices sit side by side? c) In a pack of 100 light bulbs, 10 are defective. Samples of 5 bulbs are selected randomly. How many samples conatain at least one defective bulb?

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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Question

a) In how many ways can 6 people be seated in a row of 12 sests so that here are no unoccupied seats between people.

b) In how many ways can the 9 US supreme court justices be seated for a photo-session so that none the three women justices sit side by side?

c) In a pack of 100 light bulbs, 10 are defective. Samples of 5 bulbs are selected randomly. How many samples conatain at least one defective bulb?

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A couple of comments on b).

Comment 1

Three women judges seated side by side.

It seems this should be 7!.3! The reason is that the "entity" that seats three woman could hold them in 3! different ways. Eg. Mary, Jane, Sue. But also, Jane, Mary, Sue, etc.

Comment 2

When you subtract the number of two women judges seated side-by-side you do not exclude the case where an additional woman is seated next the "double seat" entity.

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