Question

Three persons enter a railway carriage, where there are 5 vacant seats. In how many ways can they seat themselves?

Answer 1

Hint: When the first person will enter the railway carriage he will have all 5 seats available to choose from and hence 5 ways are there. And similarly when the second person enters he will have 4 seats available to choose from and hence 4 ways are there. Also when the third person will enter he will have 3 seats to choose from and hence will have 3 ways.

Complete step-by-step answer:
Clearly, the first person can occupy any of the 5 vacant seats and hence there are 5 ways in which the first person can occupy a seat.
Now the second person can occupy any of the remaining 4 vacant seats and hence there are 4 ways in which the second person can occupy a seat.
Again the third person can occupy any of the remaining 3 vacant seats and hence there are 3 ways in which the third person can occupy a seat.
Hence, by the fundamental principle of multiplication,
The required number of ways \[=5\times 4\times 3=60\].
Hence the three persons can seat themselves in 60 ways.


Note: Students can make a mistake in finding the total number of ways in which 3 passengers can sit in 5 vacant seats by adding all the ways and doing this they will get the answer as 12, hence remembering the concept of fundamental principle of multiplication is the key here. The fundamental counting principle (also called the multiplication rule) is a way to figure out the number of outcomes in a probability problem. Basically, we multiply the events together to get the total number of outcomes.