If x, y, z, t are odd natural numbers such that `x + y + z +w=20` then find the number of values of ordered quadruplet (x, y, z, t).

Options

A. 165
B. 455
C. 310
D. none of these

Explanation

To solve the problem, we need to find the number of ordered quadruplets \((x, y, z, t)\) of odd natural numbers such that \(x + y + z + t = 20\).

### Step-by-Step Solution:

1. **Express Odd Natural Numbers**:
Since \(x, y, z, t\) are odd natural numbers, we can express them in the form:
\[
x = 2l + 1, \quad y = 2m + 1, \quad z = 2n + 1, \quad t = 2p + 1
...