3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

To find the probability that the product of three digits is odd, we must understand that a product of integers is odd only if every single integer in the set is odd. If even one digit is even, the entire product becomes even.

Step 1: Identify the available digits. From the set 1, 2, 3, 4, 5, 6, 7, 8, 9, there are 5 odd digits (1, 3, 5, 7, 9) and 4 even digits (2, 4, 6, 8).

Step 2: Calculate the total number of ways to choose 3 digits out of 9. This is calculated as 9C3, which is (9 x 8 x 7) divided by (3 x 2 x 1). 9C3 = 84.

Step 3: Calculate the number of ways to choose 3 digits such that all are odd. Since there are 5 odd digits, we choose 3 from these 5. This is calculated as 5C3, which is the same as 5C2. 5C3 = (5 x 4) divided by (2 x 1) = 10.

Step 4: Calculate the probability. Probability = Number of favorable outcomes divided by total outcomes. Probability = 10 / 84.

Step 5: Simplify the fraction. Dividing both numerator and denominator by 2, we get 5 / 42.

Therefore, the probability that the product is odd is 5/42. Option C is correct.