To find the number of ways in which Rs. 22 can be distributed among four persons such that the first person gets less than Rs. 3 and the second person gets a multiple of Rs. 4, we can use the concept of generating functions.

Let's create a generating function for each person, representing the possible amounts they can receive.

1. Generating function for the first person (P1):
The first person can receive any amount less than Rs. 3, which can be represented by the polynomial (1 + x + x^2), where the powers of x represent the possible amounts (0, 1, 2).

2. Generating function for the second person (P2):
The second person can receive a multiple of Rs. 4, which can be represented by the polynomial (1 + x^4 + x^8 + ...), where the powers of x represent the multiples of 4 (0, 4, 8, ...).

3. Generating function for the third person (P3):
The third person can receive any amount between 0 and Rs. 22, which can be represented by the polynomial (1 + x + x^2 + ... + x^22).

4. Generating function for the fourth person (P4):
The fourth person can receive any amount between 0 and Rs. 22, which can also be represented by the polynomial (1 + x + x^2 + ... + x^22).

Now, we need to find the coefficient of x^22 in the product of these generating functions, as it represents the number of ways to distribute Rs. 22 among the four persons.

Multiplying the generating functions:

(P1 * P2 * P3 * P4) = (1 + x + x^2) * (1 + x^4 + x^8 + ...) * (1 + x + x^2 + ... + x^22) * (1 + x + x^2 + ... + x^22)

To find the coefficient of x^22, we need to find the terms with x^22 in the expanded form of this expression.

Simplifying the expression:

(P1 * P2 * P3 * P4) = (1 + x + x^2) * (1 + x^4 + x^8 + ...) * (1 + x + x^2 + ... + x^22) * (1 + x + x^2 + ... + x^22)
= (1 + x + x^2) * (1 + x^4 + x^8 + ...) * (1 + x + x^2 + ... + x^22)^2

Expanding and collecting like terms, we get:

(P1 * P2 * P3 * P4) = (1 + x + x^2) * (1 + x^4 + x^8 + ...) * (1 + x + x^2 + ... + x^22)^2
= (1 + 2x + 3x^2 + 4x^3 + ... + 23x^22 + ...)

The coefficient of x^22 is the coefficient of the term 23x^22, which is 23.

Therefore, the number of ways in which Rs. 22 can be distributed among four persons such that the first person gets less than Rs