In how many ways can we get a sum of atmost 15 by throwing six distincct dice?

Explanation

To solve the problem of finding the number of ways to get a sum of at most 15 by throwing six distinct dice, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the number of combinations of six distinct dice (each die can show a number from 1 to 6) such that the sum of the numbers on the dice is at most 15.

2. **Setting Up the Variables**: Let \( x_1, x_2, x_3, x_4, x_5, x_6 \) represent the values shown on the six dice. We need to satisfy the condition:
\[
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