Question

A room has 6 doors. In how many ways can a man enter the room through one door and come out through a different door?

Answer 1

You can enter through 6 ways. But you can exit from 30 ways. Because when you enter from 1 way 5 ways are open to exit everytime. So for 6 doors you can enter 6 times and you can exit 6X5=30 times..

Answer 2

Given,

Number of doors in a room = 6

To find,

The number of ways by which a man can enter the room through one door and come out through a different door.

Solution,

We can simply solve this mathematical problem using the following process:

We can calculate the number of ways by which a man can enter the room through one door and come out through a different door by using the concept of permutations and combinations, as follows;

= 6C2 x 2

(6C2 represents the total number of paired combinations possible for the 6 doors in the room and 2 is multiplied because each pair of doors can be counted twice, one door is used to enter in the first case and then used for exit in the second case)

= 6!/(4!2!) x 2

= 6!/4!

= 5x6 = 30

Hence, a man can enter the room through one door and come out through a different door in 30 different ways.