Three distinct natural numbers are chosen at random from 1 to 10. What is the probability that they are consecutive?

Explanation

The total number of ways to select 3 numbers from 10 is \binom{10}{3} = \frac{10 \times 9 \times 8}{6} = 120. The sets of 3 consecutive numbers are (1,2,3), (2,3,4), \dots, (8,9,10), making exactly 8 favorable outcomes. The probability is \frac{8}{120} = \frac{1}{15}.

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