Question

A bag contains four one-rupee coins, two twenty-five paise coins and five ten-paise 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

Answer 1

Hint: Now, to solve the problem consider cases to include at least one one-rupee coin and then find all possible ways and find all the cases to make up min Rs. 1 with only 10p or 25p denominations.

Complete step-by-step answer:
In the question, we are given a bag which contains four one-rupee coins, two twenty-five paise coins and five ten-paise coins, now we have to find the number of ways for which amount not less than Rs 1 is taken out.
So at first, we have to take cases where at least one one-rupee coin is there then if we take 0 or 1 or 2 25p coins all will be acceptable or if we take 0 or 1 or 2 or 3 or 4 or 5 ten-paise coins it will satisfy too. So, the total possible ways of choosing Rs. 1 coin is 4, 25p coins is 3, 10p coins is 6. So, the total number of ways for this situation is $4\times 3\times 6$ or 72 ways.
Now, we will not take any one-rupee coins so to make 1 rupee we have to include all the cases of 25p and 10p denominations as the total amount contained in 25p and 10p coins in 50p each thus, making 1 rupee. So, there is only 1 way for this situation.
Hence, the total number of cases is 72+1 or 73 ways.
Hence, the correct option is ‘c’.

Note: Students can also do so by first finding all possible cases of taking out and then subtracting it with ways of only taking out an amount which is less than Rs. 1.