1140 ways are there to select three person subcommittee from a club of twenty students
Solution:
Given that a club of twenty students wants to pick a three person subcommittee
To find: number of ways this can be done
We have to use combinations formula to solve the given sum
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected
The formula to calculate combinations is:
[tex]n C_{r}=\frac{n !}{(n-r) ! r !}[/tex]
where n represents the number of items, and r represents the number of items being chosen at a time
Here we have to choose 3 persons from 20 students
So, n = 20 and r = 3
[tex]\begin{aligned}&20 C_{3}=\frac{20 !}{(20-3) ! 3 !}\\\\&20 C_{3}=\frac{20 !}{17 ! 3 !}\end{aligned}[/tex]
To get the factorial of a number n ,the given formula is used,
[tex]n !=n \times(n-1) \times(n-2) \dots \times 2 \times 1[/tex]
Therefore,
[tex]20 C_{3}=\frac{20 \times 19 \times 18 \times 17 \ldots \ldots \ldots 2 \times 1}{17 \times 16 \times 15 \ldots .2 \times 1 \times 3 !}[/tex]
[tex]20 C_{3}=\frac{20 \times 19 \times 18}{3 !}=\frac{20 \times 19 \times 18}{3 \times 2 \times 1}=1140[/tex]
Thus 1140 ways are there to select three person subcommittee from a club of twenty students
