Question

A group of 12 people is traveling in three vehicles. If 4 people ride in each​ vehicle, in how many different ways can the people be assigned to the​ vehicles?

Answer 1

So, exist 34650 different ways.

Explanation:

We know that a group of 12 people is traveling in three vehicles. We know that 4 people ride in each​ vehicle.

So, for the first car we choose 4 people out of 12. Then from the remaining 8 people we choose 4 people for the second car. While the remaining 4 people will go into the third car.

Therefore, we get

`C_4^(12)\cdot C_4^8\cdot C_4^4=(12!)/(4!(12-4)!)\cdot (8!)/(4!(8-4)!)\cdot 1=495\cdot 70=34650\\`

So, exist 34650 different ways.