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# What is the total number of permutations of n different

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Director
Joined: 26 Mar 2006
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What is the total number of permutations of n different [#permalink]  28 Dec 2007, 19:36
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Question Stats:

17% (04:37) correct 83% (00:51) wrong based on 16 sessions
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???
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
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)
Manager
Joined: 15 Nov 2007
Posts: 135
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Re: Permutation with Repetition [#permalink]  29 Dec 2007, 01:13
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
Manager
Joined: 22 Jul 2008
Posts: 154
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Re: Permutation with Repetition [#permalink]  21 Aug 2008, 12:39
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
Intern
Joined: 29 Nov 2009
Posts: 7
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Re: Permutation with Repetition [#permalink]  29 Nov 2009, 01:14
What would the answer be for the same question but if number of combinations was asked ?
Re: Permutation with Repetition   [#permalink] 29 Nov 2009, 01:14
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