Question

Find the number C(10,6)

Answer 1

210.

Explanation:

Combination formula is

`nCr = (n!)/(r!(n-r)!)`

Then, we have that n = 10 and r=6:

`C(10,6) = (10!)/(6!(10-6)!)`

`C(10,6) = (10!)/(6!4!)`

To simplify calculus, we are going to use that n! = (n-1)!n = (n-2)!(n-1)n and so on.

`C(10,6) = (6!*7*8*9*10)/(6!4!)`

`C(10,6) = (7*8*9*10)/(4!)`

`C(10,6) = (5040)/(4*3*2*1)`

`C(10,6) = (5040)/(24)`

`C(10,6) = 210.`