If `n_1a n dn_2` are five-digit numbers, find the total number of ways of forming `n_1a n dn_2` so that these numbers can be added without carrying at any stage.

Explanation

To find the total number of ways of forming two five-digit numbers \( n_1 \) and \( n_2 \) such that they can be added without carrying at any stage, we can follow these steps:

### Step 1: Define the digits of the numbers
Let \( n_1 = x_1 x_2 x_3 x_4 x_5 \) and \( n_2 = y_1 y_2 y_3 y_4 y_5 \), where \( x_i \) and \( y_i \) are the digits of the numbers \( n_1 \) and \( n_2 \) respectively.

### Step 2: Understand the condition for addition without carrying
For the addition of \( n_1 \) and \( n_2 \) to occur without carrying, the sum of the corresponding digits must be less than or equal to 9:
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