A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows:

Case I:
5 students in the first car and 3 in the second.
Hence, 8 students are divided into groups of 5 and 3 in ⁸C₃ = 56 ways.

Case II:
4 students in the first car and 4 in the second.
So, 8 students are divided into two groups of 4 and 4 in ⁸C₄ = 78 ways.
Therefore, the total number of ways in which 8 students can travel is:
56 + 70 = 126