Number of ways in which RS. 18 can be distributed amongst four persons such that no body receives less than RS 4, is

Options

A. 42
B. 24
C. 4!
D. none of these

Answer

To solve the problem of distributing Rs. 18 among four persons such that no one receives less than Rs. 4, we can follow these steps:

### Step 1: Determine the minimum amount distributed
Since each of the four persons must receive at least Rs. 4, we first allocate Rs. 4 to each person.

\[ \text{Total amount given to 4 persons} = 4 \times 4 = 16 \text{ Rs.} \]

### Step 2: Calculate the remaining amount
After distributing Rs. 16, we find out how much money is left to distribute.

\[ \text{Remaining amount} = 18 - 16 = 2 \text{ Rs.} \]

### Step 3: Distribute the remaining amount
Now, we need to distribute the remaining Rs. 2 among the four persons. This can be done in two different ways:

#### Case 1: One person receives Rs. 2
In this case, we choose 1 person out of the 4 to receive the remaining Rs. 2. The number of ways to choose 1 person from 4 is given by the combination formula:

\[ \text{Ways} = \binom{4}{1} = 4 \]

#### Case 2: Two persons receive Rs. 1 each
In this scenario, we select 2 persons out of the 4 to each receive Rs. 1. The number of ways to choose 2 persons from 4 is:

\[ \text{Ways} = \binom{4}{2} = 6 \]

### Step 4: Calculate the total number of ways
Now, we add the number of ways from both cases to find the total number of ways to distribute the Rs. 18.

\[ \text{Total ways} = \text{Ways from Case 1} + \text{Ways from Case 2} = 4 + 6 = 10 \]

### Final Answer
Thus, the total number of ways in which Rs. 18 can be distributed among four persons such that nobody receives less than Rs. 4 is:

\[ \boxed{10} \]

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