$A$ committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in the committee is:

If three smallest squares are chosen at random on a chess board, then the probability of getting them in such a way that they are all together in a row or in a column is

Cards are drawn one by one at random from a well-shuffled full pack of $52$ cards until two aces are obtained for the first time. If $N$ is the number of cards required to be drawn,then $P(N = n)$,where $2 \le n \le 50$,is

If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks,then his chance of winning at least one prize is

From a well-shuffled deck of $52$ cards,$13$ cards are selected at random. The probability that the selected $13$ cards contain exactly $4$ kings 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 ————