Question

QE High school has 14 entrance doors. How many can a student

a) enter by one door and exit by a different door?

b) Enter and exit by any door?

Answer 1

The High school has 14 entrance doors.

Let denote the doors by D1,D2,...,D14.

a) enter by one door and exit by a different door?

Solution::

Here, if student enter by one door then, the student can not exit by the same door.

i.e, if student enter by D1 then, the student can exit by any one of the remaining 13 doors.

Similarly, for D2,D3,...,D14

So, if student enter by one door then, the student can exit by remaining 13 doors.

[ Here we consider exit only 13 doors, because if student enter by one door then, the student can not be able to enter by any others doors. ]

b) Enter and exit by any door?

Solution::

Here, if student enter in High school by any door then, the student can exit any of the 14 doors.

So, here if student enter by D1 then, the student can exit by any of the 14 doors.

if student enter by D2 then, the student can exit by any of the 14 doors.

Similarly, for D3,D4,...,D14

So, the total possible exit doors is

(14+14+14+14+14+14+14+14+14+14+14+14+14+14)

=14x14

=196

[ Here student can enter in High school by any door.]