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 step-by-step, we need to find the probability that a five-digit number formed by selecting five different digits from the set {1, 2, 3, 4, 5, 6, 7} is divisible by 9.

### Step 1: Determine the Sample Space
First, we need to find the total number of ways to select 5 digits from the set of 7 digits. This can be calculated using combinations:

\[ \text{Number of ways to choose 5 digits from 7} = \binom{7}{5} = \frac{7!}{5! \cdot (7-5)!} = \frac{7!}{5! \cdot 2!} = \frac{7 \times 6}{2 \times 1} = 21 \]
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