SOLUTION: 2n! divided by (n-3)! = 84n

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Question 1021025: 2n!
divided by
(n-3)!
= 84n

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
2n! divided by (n-3)! = 84n
%282n%21%29%2F%28n-3%29%21%22%22=%22%2284n

2n%21%22%22=%22%2284n%28n-3%29%21

n%21%22%22=%22%2242n%28n-3%29%21

n%28n-1%29%21%22%22=%22%2242n%28n-3%29%21

%28n-1%29%21%22%22=%22%2242%28n-3%29%21

%28n-1%29%21%22%22=%22%227%2A6%28n-3%29%21

The left side is a factorial.
For the right side to be a factorial beginning
with 7*6, it must be 7! or 7*6*5*4*3*2*1.
Then (n-3)! must be 5*4*3*2*1 or 5!

Therefore

%28n-3%29%21%22%22=%22%225%21

n-3%22%22=%22%225

n%22%22=%22%228

Checking:

%282n%21%29%2F%28n-3%29%21%22%22=%22%2284n

%282%288%21%29%29%2F%288-3%29%21%22%22=%22%2284%288%29

2%2840320%29%2F%285%29%21%22%22=%22%22672

2%2840320%29%2F120%22%22=%22%22672

672%22%22=%22%22672

So it checks:

Solution: n%22%22=%22%228

Edwin