how to solve n!

(1). n!/[11!(n-11)!]= 12376= 2^(3)* 7* 13* 17
(2). n!/[11!(n-11)!]= n*(n-1)*...*(n-10)/11!
分子為連續11個整數相乘,分母之11!必定全部可約分,
而結果= 2^(3)* 7* 13 * 17
表示約分後至少含17, 故 n= 17, 18兩者可能
n=18時 n!/[11!*(n-11)!]= 18*17*16*15*14*13*12*11*10*9*8/11!
=18*17*...*12/7!
分子含2^8分母含2^4,約分還剩2^4,與12376= 2^3*7* 13*17不合
只剩n=17可能,Check後亦成立, 故 n=17

Let me try...
n!/(11!(n-11)!) = 12376
=>n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9)(n-10)/11!=12376
=>n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9)(n-10)/11!
=2x2x2x7x13x17

checking the numerator... try factorize...
11!=11x5x2x3x3x2x2x2x7x2x3x5x2x2x3x2x1
~)
11 is eliminated, so there is 11.
~)
17 & 13 are not eliminated, so there are 17 & 13.
since continuous, so 11 to 17.
~)
there is 2 7s, so 7 to 17 or 11 to 21.
if 7 to 17, 7x2x2x2x3x3x2x5x11x2x2x3x13x2x7x3x5x2x2x2x2x17
if 11 to 21, 11x2x2x3x13x2x7x3x5x2x2x2x2x17x2x3x3x19x2x2x5x3x7
...but there is no 19 in 12376...
so numerator is 7 to 17
so n is 17.

題目等價於解 nC11 = 12376
最快既方法就係由n=11開始逐個試上去。

如果你係都要解佢出佢，咁上面條方程如果執執佢，可以變為一條11次方程。至於你有冇辦法去解一條11次方程，就有待研究……

i want the equation for solving n

應該就無公式可以解得n了。
要用trial and error的方法，即將n逐個數試試。
P.S. when n = 17
17! / [11!(17 - 11)!] = 12 376
所以n = 17