Finding 'N' when total permutations or combinations given

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msd_2008: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Sun Jun 29, 2008 8:37 pm; Location: India; Thanked: 1 times

Finding 'N' when total permutations or combinations given

by msd_2008 » Fri Dec 05, 2008 3:47 am

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

When the going gets tough, the tough gets going.

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Source: Beat The GMAT — Problem Solving | Fri Dec 05, 2008 3:47 am

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 am; Thanked: 146 times; Followed by:2 members

by parallel_chase » Fri Dec 05, 2008 11:54 am

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.

No rest for the Wicked....

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

by logitech » Fri Dec 05, 2008 12:07 pm

parallel_chase wrote:GMAT only tests logic , therefore you wont be required to calculate such values

Priceless intel!

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 am; Location: USA; Thanked: 13 times; Followed by:1 members