Question

There are $2$ gates to enter a school and $3$ staircases from first floor to the second floor. How many possible ways are there for a student to go from outside the school to a classroom on the second floor and come back ?

Answer 1

From outside to class room on second floor:

Student can go into school at $2$ ways. He can go to second floor from first floor in $3$ ways.

Since, he has to do both,

No. of ways of going to class$=2\times 3=6$

In the same $6$ ways he can come back. Since, he has to go in and come back, total no. of ways$=6\times 6=36$.