Question

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. $\frac{1}{2}$
• B. $\frac{7}{48}$
• C. $\frac{5}{42}$
• D. $\frac{5}{108}$

Answer 1

The correct option is C

$\frac{5}{42}$

Explanation for the correct answer.

Given: $1,2,3,4,5,6,7,8,9$ digits

Total numbers of three-digit numbers without repetition are $9\times 8\times 7=504$

We have to choose only odd numbers for the product to be odd.

Total number of three-digit numbers whose product is odd $=5\times 4\times 3=60$

Probability $=\frac{Totalnumberoffavourableevents}{Totalpossibleevents}$

Required probability $=\frac{60}{504}=\frac{5}{42}$

Hence option C is the correct answer.