Question 459764: How many arrangements are there of all the letters in PUPPIES if : The 3Ps must be together? The arrangement must begin and end with a P?
My work:
7P3 x 7P4 ?
3P1 x 6P5 x 3P1 ?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! You should note that the P's are indistinguishable if you are looking for distinct arrangements.
If the 3 P's must be together, we can treat the three P's as one giant letter. Then, there are four "letters" to be arranged, creating 4P4 = 24 arrangements.
If the arrangement must begin and end with a P, then we have the letters E, I, P, S, and U to arrange in the center. Here, there are 5P5 = 120 arrangements.
Note that I did not treat the P's as being distinct.
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