Question

Calculate.
12C4
Note: Cr=
n
n!
r!(n−r)!

Answer 1

495

Explanation:

using the definition

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

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12
`C_(4)`

=
`(12!)/(4!(12-4)!)`

=
`(12!)/(4!(8!))`

cancel 8! on numerator/ denominator

=
`(12(11)(10)(9))/(4!)`

=
`(11880)/(4(3)(2)(1))`

=
`(11880)/(24)`

= 495