Answer:
A
Step-by-step explanation:
Using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2).... × 3 × 2 × 1
Then evaluating numerator and denominator
10[tex]C_{3}[/tex]
= [tex]\frac{10!}{3!(7!)}[/tex]
= [tex]\frac{10(9)(8)(7)(6)(5)(4)(3)(2)(1)}{3(2)(1)(7(6)(5)(4)(3)(2)(1)}[/tex]
Cancel 7(6)(5)(4)(3)(2)(1) on numerator/ denominator, leaving
= [tex]\frac{10(9)(8)}{3(2)}[/tex] = [tex]\frac{720}{6}[/tex] = 120
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6[tex]C_{4}[/tex]
= [tex]\frac{6!}{4!(2!)}[/tex]
= [tex]\frac{6(5)(4)(3)(2)(1)}{4(3)(2)(1)(2)}[/tex]
Cancel 4(3)(2)(1) on numerator/ denominator, leaving
[tex]\frac{6(5)}{2}[/tex] = [tex]\frac{30}{2}[/tex] = 15
-------------------------------------------------------------------------------------
Dividing numerator by denominator gives
[tex]\frac{120}{15}[/tex] = 8 → A
