First slide

Combinations

Question

A bag contains four one-rupee coins, two twenty-five 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.)

Moderate

A

71
B

72
C

73
D

80

Solution

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 trventy-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.

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