Question

10 people travel in two cars, a saloon and a mini. if the saloon has seats for 6 and the mini has seats for 4, find the number of different ways in which the party can travel, asuming that the order of seating in each car does not matter and all the people can drive.

Answer 1

We're told that order doesn't matter, so we know that we're using combinations.

There are only two cars; For every combination of 4 people you fit in the mini, there's a unique combination of 6 people that would have to be in the saloon. Basically, you only need to find the different ways you can sort the 10 people into one of the cars.

So, the question simplifies to "How many ways can you select 4 people out of a group of 10 people?"