Fourteen numbered balls (1, 2, 3, …, 14) are divided in 3 groups randomly. Find the probability that the sum of the numbers on the balls, in each group, is odd.

Explanation

To solve the problem of finding the probability that the sum of the numbers on the balls in each group is odd when fourteen numbered balls (1, 2, 3, …, 14) are divided into three groups randomly, we can follow these steps:

### Step 1: Analyze the Problem
We have 14 balls numbered from 1 to 14. The sum of the numbers in each group needs to be odd. For a sum to be odd, there must be an odd number of odd numbers in that group.

### Step 2: Identify Odd and Even Numbers
Among the numbers from 1 to 14:
- Odd numbers: 1, 3, 5, 7, 9, 11, 13 (Total = 7)
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