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?
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Thank you for the detailed reply.
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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