SOLUTION: Solve this: 12(nC2) = n!

Algebra ->  Permutations -> SOLUTION: Solve this: 12(nC2) = n!      Log On


   

Question 920295: Solve this:
12(nC2) = n!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
12%28nC2%29+=+n%21

12%28n%21%2F%282%21%28n-2%29%21%29%29=n%21

12n%21%2F%282%21%28n-2%29%21%29=n%21

Multiply both sides by 2!(n-2)!

12n%21=n%212%21%28n-2%29%21

Divide both side by n!

12=2%21%28n-2%29%21

Substitute 2! = 2*1 = 2

12=2%28n-2%29%21

Divide both side by 2

6=%28n-2%29%21

3%2A2%2A1=%28n-2%29%21

3%21=%28n-2%29%21

Take the "anti-factorial" of both sides

3=n-2

5=n  <---answer!

Checking:

12%28nC2%29+=+n%21
12%285C2%29+=+5%21
12%2810%29+=+5%2A4%2A3%2A2%2A1
120-120

Edwin