Room Assignments When seven students take a trip, they find a hotel with three rooms available: a room for one person, a room for two people, and a room for three people. In how many different ways can the students be assigned to these rooms? (One student has to sleep in the car.)

To find:

The number of ways in which the students can be assigned to the rooms.

Given:

The total number of students is 7

The total number of rooms available is 3

The first room is available for 1 person.

The second room is available for 2 persons.

The third room is available for 3 persons.

It is given that one student has to sleep in the car.

Approach:

The number of permutations of n objects out of which p1 are of one kind, p2 are of second kind, pk are of kth kind and so on, is

n!p1!p2!.....