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  4. 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.)

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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.)

Permutations and Combinations

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 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 $73 .$