Question

What is C(7,3)?

Answer 1

35

Explanation:

I am pretty sure you are referring to combinatorics and specifically the combination `C_3^7`, aka `7` choose `3`, often written as `((7),(3))`.

Well:

`((n),(k)) = (n!)/((n-k)!k!)`

Which means that:

`((7),(3)) = (7!)/(4!3!)`

`= (color(red)(1 times 2 times 3 times 4) times 5 times color(blue)(6) times 7)/((color(red)(1 times 2 times 3 times 4) )(color(blue)(1 times 2 times 3)))`

`= 35`