Question

14. A school has three gates and four staircases
from the first floor to the second floor. How
many ways does a student have to go from
outside the school to his classroom on the
second floor?​

Answer 1

Answer:

12 apply Permutations and combination

Answer 2

Answer:

Hence, the total number of ways are 24.

Step-by-step explanation:

Consider the provided information.

A school has three gates and four staircases  from the first floor to the second floor.

Let say Gate A, Gate B, and Gate C.

If you enter from Gate A then you have 4 choices for staircase.

If you enter from Gate B then you have 4 choices for staircase.

If you enter from Gate C then you have 4 choices for staircase.

Therefore, the total number of ways from outside to second floor are:

(1×4)+(1×4)+(1×4)=12 Ways.

Now from second floor to outside the number of ways are:

Let say Staircase A, Staircase B, Staircase C and Staircase D.

If you exit from Staircase A then you have 3 Gates for outside.

If you exit from Staircase B then you have 3 Gates for outside.

If you exit from Staircase C then you have 3 Gates for outside.

If you exit from Staircase D then you have 3 Gates for outside.

Therefore, the total number of ways from second floor to outside are:

(1×3)+(1×3)+(1×3)+(1×3)=12 Ways.

Hence, the total number of ways are 12+12=24.