Question

There are $5$ doors in a Lecture Hall. In how many ways a student can enter the room through one door and leave through another ?

Answer 1

No. of ways a person can enter the hall through $5$ doors

$={}^5{C}_1=5$ ways

No. of way a person can exit the hall through $5$ doors

$={}^5{C}_1=5$ ways

$\therefore$ Total no. of ways $={}^5{C}_1\times {}^5{C}_1=5\times 5=25$ ways.