$A$ basket contains $12$ apples in which $3$ are rotten. If $3$ apples are drawn at random simultaneously from it,then the probability of getting at most one rotten apple is

$\omega$ is a complex cube root of unity. When an unbiased die is thrown $3$ times, if $\beta_1, \beta_2, \beta_3$ are the numbers appeared on the die, then the probability that $\beta_1, \beta_2$ and $\beta_3$ satisfy $\omega^{\beta_1}+\omega^{\beta_2}=-\omega^{\beta_3}$ is

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

$A$ box contains $2$ black,$4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box,another ball is drawn at random and kept aside the first. This process is repeated until all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black,$4$ white and $3$ red is

Out of $15$ players,there are $8$ batsmen and $7$ bowlers. What is the probability of selecting a team of $6$ batsmen and $5$ bowlers?

Three faces of a fair die are yellow,two faces are red and one face is blue. If the die is tossed $3$ times,then the probability that the colours yellow,red and blue appear is (need not be in that order).