Question

Three numbers are chosen at random from the first $20$ natural numbers. Then what is the probability that their product is odd?

Answer 1

Number of ways we can choose $3$ distinct integers from $20$ integers:

${}^{20}{C}_3=\frac{20\times 19\times 18}{3\times 2\times 1}=1140$

Product odd:odd$\times$odd$\times$odd

Number of ways we can choose $3$ distinct odd integers from $10$ odd integers:

${}^{10}{C}_3=\frac{10\times 9\times 8}{3\times 2\times 1}=120$

P$\left(productisodd\right)=\frac{120}{1140}=\frac{2}{19}$