Question

Three integers are chosen at random from the first $20$ integers. The probability that their product is even, is

• A. $\frac{2}{19}$
• B. $\frac{3}{29}$
• C. $\frac{17}{19}$
• D. $\frac{4}{29}$

Answer 1

The correct option is C $\frac{17}{19}$

The total number of ways in which $3$ integers can be chosen from first $20$ integers is ${}^{20}{C}_3$.
The product of three integers will be even if at least one of the integers is even.
Therefore, the required probability $=1-$ Probability of three integers is even
$=1-\frac{{}^{10}{C}_3}{{}^{20}{C}_3}=1-\frac{2}{19}=\frac{17}{19}$