Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is
$\frac{1}{10}$
$\frac{1}{17}$
$\frac{1}{12}$
$\frac{1}{11}$
There are $10$ engineering colleges and five students $A, B, C, D, E$ . Each of these students got offer from all of these $10$ engineering colleges. They randomly choose college independently of each other. Tne probability that all get admission in different colleges can be expressed as $\frac {a}{b}$ where $a$ and $b$ are co-prime numbers then the value of $a + b$ is
An ordinary cube has four blank faces, one face marked $2$ another marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws, is
Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that ${a^2} - {b^2}$ is divisible by $3$ is
A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ memiers) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is