Question 10

Explanation

Since each married couple must ride in the same car, we can treat each couple as a single unit. There are a total of $5$ couple units to be distributed into $2$ cars.

The capacity of each car is $6$ passengers, which is equivalent to $3$ married couples. Therefore, the number of couples in a single car cannot exceed $3$. The possible distributions of couples for Car A and Car B that satisfy the capacity constraint are:

1. Car A carries $3$ couples, Car B carries $2$ couples.
2. Car A carries $2$ couples, Car B carries $3$ couples.

For the first case, we choose $3$ couples out of the $5$ available to go into Car A. The remaining couples automatically go to Car B.

For the second case, we choose $2$ couples out of the $5$ available to go into Car A.

The total number of ways to arrange the passengers is the sum of both possibilities.