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

Explanation

Clearly, the first person can occupy any of the 5 seats.
So, there are 5 ways in which the first person can seat himself.
Now, the second person can occupy any of the remaining 4 seats.
So, the second person can be seated in 4 ways.
Similarly, the third person can occupy a seat in 3 ways.
Hence, by the fundamental principle of multiplication, the required number of ways `=(5xx4xx3)=60.`