SOLUTION: There are 12 videotapes arranged in a row on a shelf in a video shop. There are three identical copies of Gone with the wind, 4 of Tootsie and 5 of Gladiator. * (i)How many differ

Question 844392: There are 12 videotapes arranged in a row on a shelf in a video shop. There are three identical copies of Gone with the wind, 4 of Tootsie and 5 of Gladiator. *
(i)How many different arrangements of videotapes are there? (Is it 12! ?)
(ii) How many different arrangements are there if videos with the same titles are grouped together?
(iii) The 12 videotapes are arranged at random in a ow of the shelf. Find the probability that the arrangement has a copy of Gone with the Wind, at the end of one row, and a copy of Gladiator at the other end.
Thanks!! :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are 12 videotapes arranged in a row on a shelf in a video shop.
There are three identical copies of Gone with the wind, 4 of Tootsie and 5 of Gladiator.
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(i)How many different a! = 6rrangements of videotapes are there?
Ans: 12!/(3!*4!*5!) = 27720 ways
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(ii) How many different arrangements are there if videos with the same titles are grouped together?
Ans: 3! = 6
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(iii) The 12 videotapes are arranged at random in a row of the shelf. Find the probability that the arrangement has a copy of Gone with the Wind, at the end of one row, and a copy of Gladiator at the other end.
# of ways to succeed: 3*5*(10!/(2!*4!*4!)) = 47250
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Cheers,
Stan H.
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