Question

$15$ buses operate between Hyderabad and Tirupathi.The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is

• A. $15$
• B. $150$
• C. $210$
• D. $225$

Answer 1

The correct option is C $210$

While going ,number of ways to choose $1$ bus out of $15$ is ${}^{15}{C}_1$.
While return trip, in order to come with different bus, number of buses left $=14$.
Number of ways to choose $1$ bus for return trip $=$ ${}^{14}{C}_1$
So, the required number of ways for going and return $=$ ${}^{15}{C}_1{\times }^{14}{C}_1=210$