Answer:
b
Step-by-step explanation:
Evaluate using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n ! = n(n - 1)(n - 2)(n - 3)..... × 3 × 2 × 1
Given
9[tex]C_{3}[/tex]
= [tex]\frac{9!}{3!(9-3)!}[/tex]
= [tex]\frac{9.8.7.6.5.4.3.2.2.1}{3!.6!}[/tex]
= [tex]\frac{9.8.7.6.5.4.3.2.1}{3.2.1(6.5.4.3.2.1)}[/tex]
Cancel 6.5.4.3.2.1 on numerator and denominator, leaving
= [tex]\frac{9.8.7}{3.2.1}[/tex]
= [tex]\frac{504}{6}[/tex]
= 84 → b
