 QUESTION

# 4 buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are:A. 12B. 16C. 4D. 8

Hint: Find the number of ways by which the man can go to Gwalior. Similarly, find the number of ways for a return journey. He can’t use the same bus that he went to Gwalior for the return journey. Thus find the total number of ways.

$\therefore$The total number of ways in which he can travel = (number of ways from Bhopal to Gwalior) $\times$ (number of ways from Gwalior to Bhopal)
$\therefore$Total number of ways he can travel = $3\times 4=12$ ways.
$\therefore$The total number of ways he can travel = 12 ways.
Note: It is said that he has 4 buses which run between Bhopal and Gwalior. So you mistakenly will take 4 bus routes again, which means that $4\times 4=16$ ways. While he can’t travel back in the same bus which he went to Gwalior in, so return way choice is limited to 3. Remember to keep this point in mind while solving.