SOLUTION: The number of combinations of 2 objects from 'n' is equal to the number of combinations of 3 objects from 'n'. Determine 'n'.

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Question 410825: The number of combinations of 2 objects from 'n' is equal to the number of combinations of 3 objects from 'n'. Determine 'n'.
Found 2 solutions by richard1234, sudhanshu_kmr:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have nC2+=+nC3. Two ways to solve it:

Solution 1 (faster solution):
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If you know that nCk+=+nC%28n-k%29 we can set k = 2 and n-k = 3, k+%2B+%28n-k%29+=+2+%2B+3+=+5, so n = 5.

Solution 2 (algebraic solution):
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We can write it as an algebraic equation:

n%21%2F%28%28n-2%29%212%21%29+=+n%21%2F%28%28n-3%29%213%21%29

This is equivalent to

n%28n-1%29%2F2%21+=+n%28n-1%29%28n-2%29%2F3%21

1%2F2%21+=+%28n-2%29%2F3%21

1%2F2+=+%28n-2%29%2F6 --> Cross-multiplying, we get n = 5.

Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Here nC2 = nC3
=> n!/ 2! * (n-2)! = n!/3!* (n-3)!
here nominators are same so, compare denominators
2! * (n-2)! = 3! * (n-3)!
=> (n-2) = 3 [ because (n-2)! = (n-2)* (n-3)! and 3! = 3* 2! ]

=> n = 3+2 = 5

n =5