SOLUTION: Find n when nC2 = 10. I know the answer but need to show how to work it out.

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Question 684256: Find n when nC2 = 10. I know the answer but need to show how to work it out.





Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

when you have a question like nC2=10
to solve for n, you can do it this way:

n%28n-1%29%28n-2%29%2F2%21%28n-2%29%21+=+10
n%28n-1%29%2F2+=+10
n%28n-1%29+=+20
n%5E2-n-20=0....replace -n with -5n%2B4n and factor
n%5E2-5n%2B4n-20=0
%28n%2B4%29%28n-5%29=0
solutions:

if %28n%2B4%29=0 than n=-4 or
if %28n-5%29=0 than n=5 ......since n can’t be negative we use only solution n=5


check:
nCr=n%21%2F%28%28n-2%29%21%2Ar%21%29
given r=2
solve the expression nC2=n%21%2F%28%28n-2%29%21%2A2%21%29

plug in n=5+

5C2=5%21%2F%28%285-2%29%21%2A2%21%29

5C2=%285%2A4%2A3%2A2%2A1%29%2F%283%21%2A2%21%29

5C2=%285%2A4%2A3%2A2%2A1%29%2F%283%2A2%2A1%2A2%2A1%29



5C2=5%2A2

5C2=10