# 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)

98

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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:

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To find the total number of ways to give at least one rupee to the beggar:

- Use at least one 1 rupee coin: 1 way
- Use one 1 rupee coin and any combination of 25 paise and 50 paise coins:
- 1 one rupee coin + 1 of 25 paise coin + 3 of 50 paise coin = 1 way
- 1 one rupee coin + 2 of 25 paise coin + 2 of 50 paise coin = 1 way
- 1 one rupee coin + 3 of 25 paise coin + 1 of 50 paise coin = 1 way
- 1 one rupee coin + 4 of 25 paise coin = 1 way

- Use two 1 rupee coins and any combination of 25 paise and 50 paise coins:
- 2 one rupee coins + 2 of 25 paise coin + 1 of 50 paise coin = 1 way
- 2 one rupee coins + 3 of 25 paise coin = 1 way

Total number of ways = 1 (from case 1) + 4 (from case 2) + 2 (from case 3) = 7 ways.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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