Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to combine the fractions on the righthand side over the common denominator:


share|cite|improve this question
I tried with $k!(k-1)!(n-k+1)$ but I don't know how to do it with factorial – tobyyy Apr 15 '13 at 17:43


$$\begin{align} \color{red}{k!}\cdot \color{blue}{(k-1)!}\cdot \color{green}{(n-k)!} &= \color{red}{k(k-1)!}\cdot\color{blue}{(k-1)(k-2)!}\cdot\color{green}{\dfrac{(n-k+1)!}{n-k+1}}\\ &= \dfrac{\color{red}{k}\color{blue}{(k-1)}}{\color{green}{n-k+1}} \color{red}{(k-1)!}\color{blue}{(k-2)!}\color{green}{(n-k+1)!} \end{align}$$

share|cite|improve this answer

Hint: $$k!=k\cdot(k-1)!\\(k-1)!=(k+1)\cdot(k-2)!\\(n-k+1)!=(n-k+1)\cdot(n-k)!$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.