Question

The total number of ways in which a beggar can be given at least one rupee from four 25 paise coins, three 50 paise coins and 2 one rupee coins is:
A.54
B.53
C.51
D.48

Answer 1

Hint: Find the total number of ways in which the beggar can be given money, some or all. Subtract the number of ways for which the total amount is less than 1 rupee.

Complete step-by-step answer:
We are given that there are four 25 paise coins, three 50 paise coins and 2 one rupee coins.
Total number of ways to give some coins or no coins to the beggar can be calculated by multiplying the choices of the selection of the coins.
Number of ways in which we can select from four 25 paise coins is 5, as we can combine no coins, one coin, two coins, three coins and four coins.
Similarly, the number of ways in which three 50 paise can be given is 4.
Number of ways in which the one rupee coin can be given is 3.
Thus the total number of ways for giving money to beggars will be multiplication of the values 5,4 and 3.
Number of ways $5.4.3 = 60$
The denomination for which the total amount is less than one rupee is 0 , 25 paise, 50 paise and 2 rupee coin.
For 0 rupee denomination, the number of ways is 1.
For 25 paise denomination the only possible way is one coin of 25 paise.
For 50 paise denomination, two possible ways is one coin of 50 paise, and 2 coins of 25 paise.
For 75 paise denomination, the possible ways is three coins of 25 paise, one 50 paise along one 25 paise.
Thus subtracting the total of \[1 + 1 + 2 + 2 = 6\] ways from 60, we get $60 - 6 = 54$.
Hence the total number of ways in which a beggar can be given at least one rupee from four 25 paise coins, three 50 paise coins and 2 one rupee coins is 54.
Thus option A is the correct answer.

Note: Total number of ways to give some coins or no coins to the beggar can be calculated by multiplying the individual choices from the given set of coins.