Question

Divide the combinations. 60C3 / 15C3

Answer 1

The combination, nCr, which means "combination of n taken r" can be calculated by the equation,
                               nCr = n! / (n - r)!r!
where ! is a factorial sign. For the given,
                     60C3 = 60! / (60 - 3)!3! = 34220
                     15C3 = 15! / (15 - 3)!3! = 455
Their quotient is approximately 75.21.

Answer 2

I hope you know what '!' means
2!=2
3!=6
4!=24
basicalkly times every natural number including and before that number


nCr=$\frac{n!}{r!(n-r)!}$
so
$\frac{60C3}{15C3}$=
$\frac{ \frac{60!}{3!(60-3)!} }{ \frac{15!}{3!(15-3)!} }$=
$( \frac{60!}{3!(60-3)!})(\frac{3!(15-3)!}{15!})$=
$( \frac{60!}{3!(57)!})(\frac{3!(12)!}{15!})$=
$\frac{(60!)(3!)(12!)}{(3!)(57!)(15!)}$=
$\frac{(60!)(12!)}{(57!)(15!)}$=
$\frac{(60!)}{(57!)(15)(14)(13)}$=
$\frac{(60)(59)(58)}{(15)(14)(13)}$=
$\frac{(30)(59)(58)}{(15)(7)(13)}$=
$\frac{(6)(59)(58)}{(3)(7)(13)}$=
$\frac{6844}{91}$