SOLUTION: . If the number of combinations of n objects taken 3 at a time is 20, how many permutations are there?

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Question 1191918: . If the number of combinations of n objects taken 3 at a time is 20, how many permutations are there?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

C%5Bn%5D%5E3 = 20  means  %28n%2A%28n-1%29%2A%28n-2%29%29%2F%281%2A2%2A3%29 = 20,


which implies  n*(n-1)*(n-2) = 120.


It means n = 6  (easy trial and error or easy reasoning);  


hence n! = 6! = 720.


ANSWER.  720 permutations.

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The question is not clear.

Are you looking for the number of permutations of the 3 of the n objects, or the number of permutations of all n objects?

My reading of the problem suggests that the question being asked is the number of permutations of the 3 objects.

In that case, the solution is easy.



P%28n%2C3%29+=+%28n%29%28n-1%29%28n-2%29

Therefore, given C(n,3)=20, we can immediately deduce that P(n,3) is 6*20 = 120

ANSWER (the way I read the problem): 120