Question

An integer is selected at random from the set \(\{100, 101, 102, \ldots, 999\}\). What is the probability that the sum of the digits of the selected number is the same as the product of its digits?

• A. $\dfrac{1}{75}$
• B. $\dfrac{1}{150}$
• C. $\dfrac{1}{180}$
• D. $\dfrac{1}{60}$

Hint:

To solve probability questions involving digit properties, iterate through the number range with simple code or logical checks.

Answer 1

The Correct Option is B

We need to find all 3-digit numbers from 100 to 999 where the sum of the digits is equal to the product of the digits. There are 900 numbers in this range. Only 6 such numbers satisfy the condition (e.g., 123, 132, etc.). So, probability = $\dfrac{6}{900} = \dfrac{1}{150}$.