In the question, three persons entering a railway carriage where there are $5$ vacant
seats. In how many ways can they seat themselves?
Why are we multiplying $5\times 4\times 3$? Ive read the fundamental principle of counting but still I cant apply much of it in this question.
Choose one person: they have 5 places in which they can sit.
Choose the second person: they have 4 places. Likewise, the third person has three places.
Thus, $5 \times 4 \times 3$ possible arrangements.