Question

Find the value of the combination. 4C3 = _____

Answer 1

4

Explanation:

using the definition

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

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

then

4
`C_(3)`

=
`(4!)/(3!(4-3)!)`

=
`(4!)/(3!(1!))` ( note 1! = 1 )

=
`(4(3)(2)(1))/(3(2)(1))` ← cancel 3(2)(1) on numerator/ denominator

= 4