Question

There are $10$ steamers plying between Liverpool and Dublin; in how many ways can a man go from Liverpool to Dublin and return by a different steamer?

Answer 1

There are ten ways of making the first passage(since there are 10 steamers); and with each of these there is a choice of nine ways of returning (since the man is not to come back by the same steamer); hence the number of ways of making the two journeys is $10\times 9$ $=90$ or $90$.