Answer
$20_{{C}{_{3}}}$ = 1140
Work Step by Step
Total number of people in the club = 20
Number of people to be selected = 3
To find the number of ways to select 3 out of 20, we use the formula $n_{{C}{_{r}}}$ = $\frac{n!}{(n - r)! . r!}$
The number of selections = $20_{{C}{_{3}}}$ = $\frac{20!}{(20 - 3)! . 3!}$
= $\frac{20!}{17! . 3!}$
= $\frac{20\times19\times18\times17!}{17!. (3\times2\times1)}$
= $\frac{20\times19\times18}{3\times2\times1}$
= 1140
