Guys,
Can anyone please explain to me how to find 'n' when total permutations or combinations have been given?
For eg:- 10 C 4 = 210. What if the problem said N C 4 = 210, find value of N?
Similarly, 10 P 4 = 5040. What if the question said N P 4 = 5040, find the value of N ?
Regards
MSD
Finding 'N' when total permutations or combinations given
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Now those are pretty big values to calculate the combinations
Try with easy one, GMAT only tests logic , therefore you wont be required to calculate such values
Here is the basic concept:
5C2 = 10
NC2 = 10
N! / (N-2)! 2! = 10
N! / (N-2)! = 10* 2!
N! = N*(N-1)*(N-2)!
N*(N-1)*(N-2)! / (N-2)! = 20
N*(N-1) = 20
N^2 -N -20 = 0
N^2 -5N + 4N -20 = 0
(N-5) (N+4) = 0
either N can be 5 or -4, since we are calculating for combinations there can be no negative values, hence the answer is 5.
You can apply the same method in the original question.
NC4 = 210
N!/(N-4)!*4! = 210
N!/(N-4)! = 210 * 2!
N! = N*(N-1)*(N-2)*(N-3)*(N-4)!
N*(N-1)*(N-2)*(N-3)*(N-4)! / (N-4)! = 5040
N*(N-1)*(N-2)*(N-3) = 5040
You can solve for N to find its value.
If GMAT gives you such big numbers, which is very unlikely but nevertheless you can insert the answer options to find the solution.
Hope this helps.
Try with easy one, GMAT only tests logic , therefore you wont be required to calculate such values
Here is the basic concept:
5C2 = 10
NC2 = 10
N! / (N-2)! 2! = 10
N! / (N-2)! = 10* 2!
N! = N*(N-1)*(N-2)!
N*(N-1)*(N-2)! / (N-2)! = 20
N*(N-1) = 20
N^2 -N -20 = 0
N^2 -5N + 4N -20 = 0
(N-5) (N+4) = 0
either N can be 5 or -4, since we are calculating for combinations there can be no negative values, hence the answer is 5.
You can apply the same method in the original question.
NC4 = 210
N!/(N-4)!*4! = 210
N!/(N-4)! = 210 * 2!
N! = N*(N-1)*(N-2)*(N-3)*(N-4)!
N*(N-1)*(N-2)*(N-3)*(N-4)! / (N-4)! = 5040
N*(N-1)*(N-2)*(N-3) = 5040
You can solve for N to find its value.
If GMAT gives you such big numbers, which is very unlikely but nevertheless you can insert the answer options to find the solution.
Hope this helps.
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- logitech
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Priceless intel!parallel_chase wrote:GMAT only tests logic , therefore you wont be required to calculate such values
LGTCH
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