點解 0! = 1 ?

By the definition of nCr

nCr=n!/[(n-r)!xr!]

the first term of the binomial expression (x+1)^n is

(nCn)x^n

=n!/n!(0!)x^n

If 0! <> 1 , then the first and the last term 's coeff. is not 1 , and it is not true.

So 0! must equal to 1 , you may treat it as definition too.

除左上面所答的, recurrence relation
圖片參考：http://upload.wikimedia.org/math/0/4/f/04f0de9cd29fc21e0bb3bf57a31a760b.png
works for n = 0 之外.
我試下用中五學生可以理解的例子來答!

nCr, 學左啦!

nCr = n! / (r!)(n-r)!
咁如果n=0, r又=0,

圖片參考：http://upload.wikimedia.org/math/6/1/c/61c7fc770aebe276db140466fabdd954.png

雖然用nCr來解factorial,唔可以叫好好.
不過, 希望你可以明啦!

呢個係定義，無得解 ...

有左呢個定義，可以帶來一些運算上的便利，如 (n + 1)! = n! * (n + 1) ，或者其他 combination / permutation 的計算。