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)   (Show Source): You can put this solution on YOUR website!





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







ANSWER: n=7

CHECK: C(7,2)=21; C(6,2)=15. 21 = 15+6
Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.

The Math translation is this equation


     =  + 6,

or

     =  + 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.




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