Question

How to find the value of the combination? Show your work! Thansk!

Answer 1

Answer:

A

Step-by-step explanation:

Using the definition

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

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

Then evaluating numerator and denominator

10$C_{3}$

= $\frac{10!}{3!(7!)}$

= $\frac{10(9)(8)(7)(6)(5)(4)(3)(2)(1)}{3(2)(1)(7(6)(5)(4)(3)(2)(1)}$

Cancel 7(6)(5)(4)(3)(2)(1) on numerator/ denominator, leaving

= $\frac{10(9)(8)}{3(2)}$ = $\frac{720}{6}$ = 120

-------------------------------------------------------------------------------------

6$C_{4}$

= $\frac{6!}{4!(2!)}$

= $\frac{6(5)(4)(3)(2)(1)}{4(3)(2)(1)(2)}$

Cancel 4(3)(2)(1) on numerator/ denominator, leaving

$\frac{6(5)}{2}$ = $\frac{30}{2}$ = 15

-------------------------------------------------------------------------------------

Dividing numerator by denominator gives

$\frac{120}{15}$ = 8 → A