Solve (n!)/(8!(n-8)!) = (n!)/(16!(n-16)!) algebraically?
I got a solution of n=21 , but I had to use the guess and check method.
I got a solution of
1 Answer
Explanation:
We have
As
Leaving us with a much simpler equation:
We can write this as:
One clear solution of this is obtained by letting
From which we get that
But is this the only solution? To check this, let
Through the definition of a factorial,
Using this new notation:
We can see that the left hand side product has exactly
From which we get that