Question

Evaluate C(9, 3). a)504 b)84 c)60480 d)5040

Answer 1

b

Explanation:

Evaluate using the definition

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

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

Given

9
`C_(3)`

=
`(9!)/(3!(9-3)!)`

=
`(9.8.7.6.5.4.3.2.2.1)/(3!.6!)`

=
`(9.8.7.6.5.4.3.2.1)/(3.2.1(6.5.4.3.2.1))`

Cancel 6.5.4.3.2.1 on numerator and denominator, leaving

=
`(9.8.7)/(3.2.1)`

=
`(504)/(6)`

= 84 → b