Question

There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms

Answer 1

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, 7C1 x 6C2 x 4C4 

= 7 x 15 x 1 = 105

Answer 2

Answer: 105 ways

Step-by-step explanation:

This can be solved using combination.

Starting with the single room, only one among the seven persons can fit there.

This can be represented as follows:

7C1 - means we are selecting just one person out of all the seven persons.

Next, considering the double room,only two among the remaining six persons can fit there.

This can be represented as follows:

6C2- means we are selecting only two persons out of the remaining six persons.

Finally, considering the four persons room, the remaining four persons can fit there.

This is represented as follows:

4C4

So now combining all the possibilities together we get:

The number of ways in which the seven persons can be arranged is:

7C1 × 6C2 × 4C4 = 7 × 15 × 1 = 105