A bag contains four one-rupee coins, two twentyfive paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.)

Question

A bag contains four one-rupee coins, two twentyfive paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.) (A) 71 (B) 72 (C) 73 (D) 80

Tardigrade Admin · Accepted Answer

When at least one one-rupee coin is selected, we can select any number of twenty-five coins and ten paisa coins. Then number of ways of such selection is

4 (2 + 1) (5 + 1) = 72

as we can select zero or more twenty-five paisa and ten paisa coins to ensure that amount selected is Rs.

1

or more.
But when none of one-rupee coins is selected we have to select all twenty-five paisa coins and ten paisa coins to ensure sum of Rs.

1

, which can be done only in one way. Then the total number of ways is

73.

Q. A bag contains four one-rupee coins, two twentyfive paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.)

71

72

73

80