combination and permutation questions

Question

nC₅=252

Answer 1

n!/5!(n-5)!=252

n!/(n-5)!=252*5!

n!/(n-5)!=252*5*4*3*2*1

n!/(n-5)!=30,240

n!/(n-5)!=n(n-1)(n-2)(n-3)(n-4) (both [n-5]! cancel)

factor 30,240

30,240=2*2*2*2*2*3*3*3*5*7

group the factors to get (2*3)*7*(2*2*2)*(3*3)*(2*5)=6*7*8*9*10

n(n-1)(n-2)(n-3)(n-4)=30,240

10*9*8*7*6=30,240

n=10

 

Answer 2

All you need to do, presumably, is to figure out what n is.  It must be >6 because 6C5 = 6, so just try it on the calculator...my first guess was 10C5 but if you want to try another n, go ahead..it won't take very long to strike paydirt.