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

• n=20
• r=5

Use combination

total ways

`\\ \rm\dashrightarrow ^nC_r=(n!)/(r!(n-r)!)`

`\\ \rm\dashrightarrow ^(20)C_5`

`\\ \rm\dashrightarrow (20!)/(5!15!)`

`\\ \rm\dashrightarrow (20(19)(18)(17)(16)(15!))/(5(4)(3)(2)(15!)`

`\\ \rm\dashrightarrow 15504`

Answer 2

• 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