The bag $\mathrm{A}$ contains $5$ blue and $6$ red balls, bag $\mathrm{B}$ contains $7$ blue and $5$ red balls. If $6$ balls are drawn at random from each of the bags, find the product of the probability that $4$ blue and $2$ red balls are drawn from bag $\mathrm{A} \mathrm{and} 3$ blue and $3$ red balls are drawn from bag $\mathrm{B}$.

Six persons $A, B, C, X, Y \& Z$ go for an interview. What is the probability of selection of $A$ and $Y$ in the interview?

In a college, $\frac{1}{5}th$ of the girls and $\frac{1}{8}\mathrm{th}$ of the boys took part in a social camp. The total number of students in the college took part in the camp is:

If $\mathrm{P}\left(\mathrm{A}\right)=\frac{2}{3}$, $\mathrm{P}\left(\overline{ \mathrm{A}} \right)$ is

There are $6$ defective items in a sample of $20$ items. One item is drawn at random. The probability that it is a non-defective item is: