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. 12 B. 16 C. 4 D. 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.
Complete step-by-step answer: It is said that 4 buses run between Bhopal and Gwalior. Thus the man can get in any one of the three buses and go to Gwalior. Thus the man has 4 ways possible to go from Bhopal to Gwalior. Thus the number of ways in which the man goes from Bhopal to Gwalior = 4 ways. Now it is said that the man comes back in another bus. There were a total of 4 buses. He took one bus out of 4 buses to go to Gwalior. Now there are 3 buses remaining. Out of these buses, he took one bus for the return journey to Bhopal. Thus the number of ways in which the man can come back from Gwalior to Bhopal = 3 ways. Thus he can go from Bhopal to Gwalior in 4 ways and he can come back to Bhopal as return journey in 3 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. Option A is the correct answer.
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.