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What is the total number of permutations of n different

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Director
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What is the total number of permutations of n different [#permalink]

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New post 28 Dec 2007, 20:36
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What is the total number of permutations of n different things taken not more than p times, when each thing may be repeated any number of times?

A. n^p +1
B. n(n^p-1)
C.n^p (n+1)/(n-1)
D. n(n^p - 1)/ (n-1)
E. n^p (n+1)

Do we have an explanation for this???

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CEO
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Concentration: Entrepreneurship, Other
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 [#permalink]

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New post 28 Dec 2007, 21:34
D

p=1: N=n
p=2: N=n*n
.....
p=p: N=n^p

M=∑N=n+n^2+...+n^p=n(n^p-1)/(n-1)

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Manager
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Re: Permutation with Repetition [#permalink]

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New post 29 Dec 2007, 02:13
Beyond700 wrote:
What is the total number of permutations of n different things taken not more than p times, when each thing may be repeated any number of times?

A. n^p +1
B. n(n^p-1)
C.n^p (n+1)/(n-1)
D. n(n^p - 1)/ (n-1)
E. n^p (n+1)

Do we have an explanation for this???


does anyone think this problem could be seen on the gmat? seems overkill

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Manager
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Re: Permutation with Repetition [#permalink]

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New post 21 Aug 2008, 13:39
If there is only one thing picked, it could be any of the n things.
If 2 things are picked, each of them coulod be any of the n things; therefore, it could be done in n^2 ways.
3 things: n^3 ways and so on and so forth.
Therefore, upto p things could be picked in n + n^2 + n^3 +...........n^p ways.
This is a GP and the sum is n (n^p - 1)/n-1

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Re: Permutation with Repetition [#permalink]

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New post 29 Nov 2009, 02:14
What would the answer be for the same question but if number of combinations was asked ?

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Re: What is the total number of permutations of n different [#permalink]

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New post 03 Jun 2016, 10:17
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Re: What is the total number of permutations of n different   [#permalink] 03 Jun 2016, 10:17
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