Question

We have 5 distinct breakout rooms and 30 distinct students in the lab. How many ways can we distribute 30 distinct students into the 5 breakout rooms? (Breakout rooms can be empty.)

A) 30
B) 5
C) 2³⁰
D) 5³⁰

Answer 1

The number of ways to distribute 30 distinct students into 5 breakout rooms is option D) 5³⁰.

Step-by-step explanation:

To distribute 30 distinct students into 5 breakout rooms, we can consider each student as having 5 choices of breakout rooms to be assigned to. Therefore, for each student, there are 5 possibilities. Since there are 30 students in total, the total number of ways to distribute the students is 5 to the power of 30.

So, the correct answer is option D) 5³⁰.