Question

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

Answer 1

A

Explanation:

Using the definition

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

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

Then evaluating numerator and denominator

10
`C_(3)`

=
`(10!)/(3!(7!))`

=
`(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

=
`(10(9)(8))/(3(2))` =
`(720)/(6)` = 120

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

6
`C_(4)`

=
`(6!)/(4!(2!))`

=
`(6(5)(4)(3)(2)(1))/(4(3)(2)(1)(2))`

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

`(6(5))/(2)` =
`(30)/(2)` = 15

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

Dividing numerator by denominator gives

`(120)/(15)` = 8 → A