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

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to through $9$ from both dice will be avoided the prize. If $A$ throws first then the probability that $B$ wins the game is

Mr. $A$ has six children and atleast one child is a girl, then probability that Mr. $A$ has $3$ boys and $3$ girls, is -
 

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. Probability that no two of them are consecutive is -

If four vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

A bag contains $20$ coins. If the probability that bag contains exactly $4$ biased coin is $1/3$ and that of exactly $5$ biased coin is $2/3$,then the probability that all the biased coin are sorted out from the bag in exactly $10$ draws is