# Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise)

##### 1 Answer

98

#### Explanation:

There are nine coins in total. I can choose to give one, some, or all of the coins to the beggar. Since each choice for each coin is a yes/no, I can use

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To check this, let's say we have 3 coins called A, B, C. We should have

A

B

C

AB

BC

AC

ABC

none

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How many ways out of the 128 makes a rupee?

One way to do this is to count the number directly and the other is to figure out how many ways we don't make a rupee and subtract that from 128. I think I'll approach this by not going over 1 rupee.

What are the different coin combinations that will keep us under? Each of these, being a combination, will fall under this general equation:

1 X 25 paise

2 X 25 paise

3 X 25 paise

1 X 50 paise

1 X 50 paise + 1 X 25 paise

We can evaluate each of these:

**1 X 25 paise**

**2 X 25 paise**

**3 X 25 paise**

**1 X 50 paise**

**1 X 50 paise + 1 X 25 paise**

Let's add them up:

**Finalizing up**

We start with 128 ways to hand out coins. We need to subtract 1 to account for not having any coin, then another 29 for handing out coins that are insufficient to reach 1 rupee. This leaves us with: