SOLUTION: The number of combinations of n items taken 2 together is 6 larger than the number of combinations of n - 1 items taken 2 together. Determine n. Not sure how to solve.

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Question 1185837: The number of combinations of n items taken 2 together is 6 larger than the number of combinations of n - 1 items taken 2 together.
Determine n.
Not sure how to solve.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


C%28n%2C2%29=%28%28n%29%28n-1%29%29%2F2
C%28n-1%2C2%29=%28%28n-1%29%28n-2%29%29%2F2

C(n,2) is 6 more than C(n-1,2):

%28%28n%29%28n-1%29%29%2F2=%28%28n-1%29%28n-2%29%29%2F2%2B6
n%28n-1%29=%28n-1%29%28n-2%29%2B12
n%5E2-n=n%5E2-3n%2B2%2B12
2n=14
n=7

ANSWER: n=7

CHECK: C(7,2)=21; C(6,2)=15. 21 = 15+6

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

The Math translation is this equation


    C%5Bn%5D%5E2 = C%5Bn-1%5D%5E2 + 6,

or

    %28n%2A%28n-1%29%29%2F2 = %28%28n-1%29%2A%28n-2%29%29%2F2 + 6.


Multiply by 2 both sides and simplify


    n*(n-1) = (n-1)*(n-2) + 12

    n*(n-1) - (n-1)*(n-2) = 12

    (n-1) * [n - (n-2)]   = 12

    (n-1) * 2             = 12

     n-1                  = 6

      n                   = 7.    ANSWER

Solved and explained.