Question

Three integers are chosen at random without replacement from the first $20$ integers. The probability that their product is odd is

Answer 1

Three integers choses at random without replacement.

Total $=20\times 19\times 18=6840$

Total odd integers

$1,3,5,7,9,11,13,15,17,19$

Total $10$ integer $=10\times 9\times 8$

Probability $=\frac{10\times 9\times 8}{6840}=\frac{4}{38}$