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: To solve this question, we are asked for the total number of ways of getting an amount, not less than Rs. \[1\], i.e., one or more than one, be taken out from the bag, so first we will consider the cases where we will first take the cases where one rupee coin is consider first, and the other coins are taken secondary, then in the second case, where we are not considering choosing one rupee coin, then here we will consider taking twenty five coin and ten paise coins only. Hence, taking all the possible cases, we will get our required answer.

Complete step-by-step answer:
We have been given that a bag contains four one-rupee coins, two twenty-five paise coins, and five ten-paise coins. We need to find the number of ways an amount, not less than Rs. \[1\] be taken out from the bag.
There are two conditions, first is when one one-rupee coin is taken, so the possible case of choosing \[1\] rupee coin is \[4,\] if we choose \[25\] paisa coin, then there is \[0,{\text{ }}1\] or \[2,\] i.e., \[3\]possibilities of choosing twenty-five paisa coin, or if we choose \[10\] paisa coin, then there is \[0,1,2,3,4\] or \[5,\] i.e., \[6\] possibilities of choosing ten-paisa coin.
So, for this case, total number of ways $ = 4 \times 3 \times 6 = 72$
Now, the second case is when, we choose not \[1\] rupee coins, then we have to include the cases of choosing \[25\] paisa coins and \[10\] paisa coins, as there are two twenty-five paise coins, and five ten-paise coins, together making one rupee.
So, for this case, total number of ways $ = 1 \times 1 = 1$
Hence, if we consider all the number of ways is \[72 + 1{\text{ }} = {\text{ }}73\]
Thus, option (C) \[73,\] is correct.
So, the correct answer is “Option C”.

Note: Students should read the question carefully first, here we are asked about finding the many ways an amount, not less than Rs. \[1\] be taken out from the given bag. So, in all the possible cases the amount should be one or more than one. So, we have to calculate in the way, where we don’t get the amount less than one.