Question

A room has 7 doors. In how many ways can a person enter through one door and come out through a different door?

• A. $30$
• B. $49$
• C. $42$
• D. $36$

Answer 1

The correct option is C $42$

Given that,
There are $7$ doors in a room.

According to question, a person can enter the room from any of the $7$ doors.

So, their are $7$ ways of entering the room as shown:


Now, after entering the room, person can come out from any of the remaining $6$ doors.

So, there are $6$ ways of coming out from the room.

We have to find the total number of ways of entering and coming out through the room.

We get,
Total number of ways $=7\times 6=42$