Question: Four integers are randomly selected from 0 to 50 inclusive. Let $z$ be the product of the four numbers. What is the probability that $z$ is divisible by 5?

Mon, 04 May 2026 22:41:19 +0000

**Four integers are randomly selected from 0 to 50 inclusive. Let $z$ be the product of the four numbers. What is the probability that $z$ is divisible by 5?** Fascinated by patterns in chance and everyday math puzzles, curious users often wonder: What’s the real likelihood that the product of four randomly chosen integers between 0 and 50 ends with a factor of five? With curiosity growing around intuitive probability and real-world applications, this question reflects broader interest in how randomness shapes outcomes—especially when invisible factors like multiples of 5 influence results. **Welcome to the quiet math behind everyday odds** When selecting four integers from 0 to 50, each value has an equal chance of being picked. The product $z$ is only divisible by 5 if at least one of those numbers includes a factor of 5—meaning it’s a multiple of 5 (e.g., 0, 5, 10, ..., 50). Since 0 multiplied by any number yields zero—a result divisible by 5—this case immediately contributes to success. Beyond 0, multiples of 5 occur at intervals of 5, giving five options each decade. This pattern shapes the probability in predictable ways.