Suppose that an operating room needs to handle three knee, four hip, and five shoulder injuries.
a) how many diff sequences are possible?
how many diff sequences have all hip, knee, and shoulder surgeries scheduled consecutively
c) how many different schedules begin and end with a knee injury

im stuck on

a) i got 12! / ( 3! * 4! * 5!)

its been a while since ive done these but:

each knee hip and shoulder injury is a unique case....

how many knee injuries can be formed if each is unique: 3!
how many hip---------------------------------------------------: 4!
how many shoulder---------------------------------------------: 5!

how many ways can you arrange these three "types" of injuries so that all the "types" are together: 3!

so there are 3!3!4!5! ways for b ) to happen-----I think

/e for c)

_ _ _ _ _ _ _ _ _ _ _ _ <-- each one of those is a spot on the schedule
the first spot must be a 3 because there must be a knee injury there and there are 3 possible knee injuries
the last spot must be a 2 because there must be a knee injury there and one is already used up at the first spot
the middle spots it doesn't matter so 10! in the middle
so I would think the answer is 3!10!

This post was edited by brigadier on Jun 4 2014 11:05pm

diz nikka