The letter of the word `$ASSASSIN$' are written down at random in a row. The probability that no two $S$ occur together is

All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is 

A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-

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

Three squares of a chess board are chosen at random, the probability that two are of one colour and one of another is

A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is ${P_1}$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is ${P_2}.$ Then