A class has 30 students. The class needs to select 3 representatives. In how many ways can this be done?

Question: A class has 30 students. The class needs to select 3 representatives. In how many ways can this be done?

Solution:
Given that,
Total students = 30
Representatives to be selected = 3

The number of ways to choose 3 representatives from 30 students is = ³⁰C₃
= 30!/{3!(30 - 3)!}
= (30 × 29 × 28 × 27!)/(3 × 2 × 27!)
= (30 × 29 × 28)/6
= 5 × 29 × 28
= 4060

Therefore, the 3 representatives can be selected in 4060 ways.