1.  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?

A. 9
B. 26
C. 126
D. 3920

Answer: Option C

Explanation:

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

Case II: 4 students in the first car and 4 in the second

Hence, in Case I: 8 students are divided into groups of 5 and 3 in 8C3 ways.

Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4 ways.

Therefore, the total number of ways in which 8 students can travel is:

(8C3 + 8C4) = 70 + 56 = 126