The total number of ways in which a beggar can be given at least one rupee from four 25 p. coins, three 50 p. coins and 2 one rupee coins is

The following four cases are there:(A) At least one one rupee coin and any number of other coins = 2 × 4 × 5 = 40 ways.(B) At least two 50 p. coins and any number of 25 p. coins = 2 × 5 = 10 ways.(C) One 50 p. coin and at least two 25 p. coins = 1 × 3 = 3 ways.(D) Four 25 p. coins in one way only ∴ total = 54.