3. Three digits are chosen at random from 1 2 3 4 5 6 7 8 9 Without repeating any digit. What is the probability that the product is odd? A. \( 2 / 3 \) B. \( 7 / 48 \) C. \( 5 / 42 \) D. \( 5 / 108 \)

We begin by noting that the product of three numbers is odd if and only if each number is odd. - **Step 1:** Determine the total number of ways to choose 3 digits from 9. The total number of combinations is \[ \binom{9}{3} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84. \] - **Step 2:** Identify the odd digits among the given digits. The odd digits are \(1, 3, 5, 7, 9\) (5 digits in total). - **Step 3:** Determine the number of ways to choose 3 odd digits from these 5. The number of favorable combinations is \[ \binom{5}{3} = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10. \] - **Step 4:** Calculate the probability that the product is odd. The probability is given by the ratio of favorable outcomes to total outcomes: \[ \text{Probability} = \frac{10}{84} = \frac{5}{42}. \] Thus, the probability that the product is odd is \(\frac{5}{42}\).