Five different digits from the set of numbers {1, 2, 3, 4, 5, 6, 7} are written in random order. Find the probability that five-digit number thus formed is divisible by 9.

Explanation

To solve the problem of finding the probability that a five-digit number formed from five different digits selected from the set {1, 2, 3, 4, 5, 6, 7} is divisible by 9, we can follow these steps:

### Step 1: Determine the Sample Space
The sample space consists of all possible ways to select and arrange 5 digits from the 7 available digits.

1. **Choose 5 digits from 7**: The number of ways to choose 5 digits from 7 is given by the combination formula \( \binom{n}{r} \):
\[
\binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7!}{5! \cdot 2!} = \frac{7 \times 6}{2 \times 1} = 21
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