Question

There are 20 machines at the gym and Manuel wants to perform exercises on 5 different machines while he is there. How many different ways can he select the machines to use?
31008

1860480

100

15504

Answer 1

• Total machines: 20

• Required: on 5 different machines

Selection of machines is persons choice and not arranged specifically, thus we will use Combination.

⇒ 20C5

⇒ 20!/5!(20-5)!

⇒ 15504

Answer 2

• n=20
• r=5

Use combination

total ways

$\\ \rm\dashrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}$

$\\ \rm\dashrightarrow ^{20}C_5$

$\\ \rm\dashrightarrow \dfrac{20!}{5!15!}$

$\\ \rm\dashrightarrow \dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(15!}$

$\\ \rm\dashrightarrow 15504$