A committee of five is to be chosen from a group of $9$ people. The probability that a certain married couple will either serve together or not at all, is

If a leap year is selected at random, what is the change that it will contain $53$ Tuesdays ?

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$, respectively. Suppose $\alpha$ is the number of heads that appear when $C _1$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C _2$ is tossed twice, independently, Then probability that the roots of the quadratic polynomial $x^2-\alpha x+\beta$ are real and equal, is

Probability that  the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ is equal to

A bag contains $4$ white, $5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white, a red and a green ball is drawn is

A box $'A'$ contanis $2$ white, $3$ red and $2$ black balls. Another box $'B'$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $'B'$ is