Question

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

Answer 1

Answer:

b

Step-by-step explanation:

Evaluate using the definition

n$C_{r}$ = $\frac{n!}{r!(n-r)!}$

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

Given

9$C_{3}$

= $\frac{9!}{3!(9-3)!}$

= $\frac{9.8.7.6.5.4.3.2.2.1}{3!.6!}$

= $\frac{9.8.7.6.5.4.3.2.1}{3.2.1(6.5.4.3.2.1)}$

Cancel 6.5.4.3.2.1 on numerator and denominator, leaving

= $\frac{9.8.7}{3.2.1}$

= $\frac{504}{6}$

= 84 → b