Permutation Question Please Help

Question

1. How many different ways can 150 guests be divided into 15 groups of 5 for a dance activity at an event?

Answer 1

There will be 75 participants in the activity, so we start with ₁₅₀C₇₅ , which gives the number of distinct dancing groups. Then, there are ₇₅C₅ ways to choose group 1, ₇₀C₅ ways to choose group 2, ₆₅C₅ ways to choose group 3, etc. on down until ₁₀C₅ ways to choose the 14th group. We can stop there because the 15th group is already chosen, since ₅C₅ = 1.

Multiplying all of the above numbers together gives the answer, which is likely outrageously big.