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

Answer:

36

Step-by-step explanation:

Hi,

Let A be the position outside , from where the student

enters the school

Let F be the position on the first floor

Let C be the classroom

Now, given that there are 2 gates to reach F from A

So, a student can choose any of the two, so there are

2 possible ways of going from A to F

Given that there are 3 staircases from which a student

can go from first floor to classroom in second floor,

So, a student can choose any of the staircases, so there are

3 possible ways of going from F to C

Hence, total number of ways a student can go from

outside the school to his class room are

= Total number of ways of student going from A to F *

  Total number of ways Student going from F to C

= 2 * 3

= 6

Similarly, for a student to come back, student  can be

back from C to F using any of 3 staircases and from F

to A by using any of the two gates,

So total number of ways in which student can get  outside

from the classroom are 3*2 = 6

Total number of ways of student going from outside to

Classroom AND getting back outside from Classroom are

= Number of ways of going from A to C *

Number of ways of going back from C to A

= 6 * 6

36.

Hence, possible ways are 36.

Hope, it helps !