SOLUTION: 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

Algebra ->  Permutations -> SOLUTION: 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      Log On


   



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) About Me  (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.