Reducing formula with factorials

Question

I'm still a beginner working with factorials so, how should I reduce this formula i.e(cancel some member to make numbers smaller) ?

$$\dfrac{(n^2)!}{4!(n^2 - 4)!\cdot Q}$$

If you say $y=n^2$ then your formula becomes $$\frac{y!}{4!\cdot(y-4)!\cdot Q}.$$ Is it easier to see how to simplify that formula? — MJD, Sep 29 '13 at 02:49

score 3 · Accepted Answer · answered Sep 29 '13 at 02:53

3

Note that

$$(n^2)! = n^2 (n^2 - 1)(n^2 - 2)(n^2 - 3) (n^2 - 4)!$$

So your formula can be reduced to

$$\frac{n^2 (n^2 - 1)(n^2 - 2)(n^2 - 3)}{24Q}$$

answered Sep 29 '13 at 02:53

1 Answers1