Two numbers are selected at random (without replacement) from first 7 natural numbers. If X denotes the smaller of the two numbers obtained, find the probability distribution of X. Also, find mean of the distribution.

Explanation

To solve the problem, we need to find the probability distribution of the smaller number \( X \) when two numbers are selected at random from the first 7 natural numbers (1, 2, 3, 4, 5, 6, 7). We will also calculate the mean of this distribution.

### Step-by-Step Solution:

1. **Identify the Sample Space**:
The first 7 natural numbers are {1, 2, 3, 4, 5, 6, 7}. When selecting 2 numbers without replacement, the total number of ways to choose 2 numbers from 7 is given by the combination formula:
\[
\text{Total combinations} = \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21
...