Question 423349
If you mean <sub>6</sub>C<sub>4</sub> then keep reading. If not, then please re-post you question.<br>
<sub>n</sub>C<sub>r</sub> = {{{n!/(r!*(n-r)!)}}}
So
<sub>6</sub>C<sub>4</sub> = {{{6!/(4!*(6-4)!)}}}
which simplifies to
<sub>6</sub>C<sub>4</sub> = {{{6!/(4!*2!)}}}
The exclamation points indicate factorials. A factorial of a (non-negative) number is the product of all the integers from 1 to the number. So
6! means 1*2*3*4*5*6
4! means 1*2*3*4
and
2! means 1*2
(P.S. 1! and 0! are both defined to be a 1.)<br>
So
<sub>6</sub>C<sub>4</sub> = {{{6!/(4!*2!) = (1*2*3*4*5*6)/((1*2*3*4)*(1*2))}}}
A lot of these factors cancel so we don't have to do very much multiplying to simplify:
<sub>6</sub>C<sub>4</sub> = {{{6!/(4!*2!) = (1*2*3*4*5*6)/((1*2*3*4)*(1*2)) = (1*cross(2)*cross(3)*cross(4)*5*6)/((1*cross(2)*cross(3)*cross(4))*(1*2)) = (5*6)/(1*2) = 30/2 = 15}}}