Dividing Binomial Coefficient

Question

I have a problem which requires multiplying:

$$ \frac 1 4 \cdot \binom n k $$

Expanded: $$ \frac 1 4 \cdot \frac {(n)!} {5!(n-5)!} $$

The answer is below, but it isn't clear how to get from the initial state to this one algebraically. $$ \frac {(n-1)!} {4!(n-5)!} $$

Yes Viram, n=20. I'm not sure how to get from one the original equation to the other one algebraically. — user1795609, Jul 09 '14 at 05:34

score 0 · Answer 1 · answered Jul 09 '14 at 06:23

0

If $n=20$ then $$\frac{1}{4}\cdot\frac{n!}{5!\cdot(n-5)!}=\frac{1}{4}\cdot\frac{20!}{5!\cdot15!}=\frac{20\cdot19!}{4\cdot5\cdot4!\cdot15!}=\frac{19!}{4!\cdot15!}=\frac{(n-1)!}{4!\cdot(n-5)!}$$

answered Jul 09 '14 at 06:23

Silynn

1,822

Would there be any way to derive the solution without knowing n = 20? – user1795609 Jul 09 '14 at 09:03
It's simply either not true for $n\neq 20$, or the requirements for it to be true result in something not very useful. – Silynn Jul 09 '14 at 10:42

Dividing Binomial Coefficient

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