Mr. A has six children and atleast one child is a girl, then probability that Mr. A has $3$ boys and $3$ girls, is
$\frac{20}{63}$
$\frac{1}{3}$
$\frac{5}{11}$
$\frac{1}{32}$
$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?
Two numbers $x$ $\&$ $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, ......, 1000\}$. Then the probability that $|x^4 - y^4|$ is divisible by $5$, is -
$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is
A bag contains, $7$ different Black balls .and $10$ different Red balls, if one by one ball are randomely drawn untill all black balls are not drawn, then probability that this process is completed in $12 ^{th}$ draw, is equal to
Three mangoes and three apples are in a box. If two fruits are chosen at random, the probability that one is a mango and the other is an apple is