Question

The formula for the

number of possible ways to choose r objects
from a set of n objects is
n!/r!(n-r)!
How
many different ways can you choose a group
of 3 students from a group of 8 students?
A. 24
B. 56
C. 120
D. 336

Answer 1

B

Explanation:

note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1

using n = 8 and r = 3 in the combination formula

`(8!)/(3!(8-3)!)`

=
`(8(7)(6)(5)(4)(3)(2)(1))/(3(2)(1)5!)` ← cancel 5! on denominator with 5(4)(3)(2)(1) on numerator

=
`(8(7)(6))/(3(2)(1))`

=
`(56(6))/(6)` ← cancel 6 on numerator/ denominator

= 56