$A$ bag contains $4$ white,$5$ red and $6$ green balls. Three balls are picked up randomly. The probability that a white,a red and a green ball is drawn 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

There are $10$ engineering colleges and five students $A, B, C, D, E$. Each of these students received an offer from all of these $10$ engineering colleges. They randomly choose a college independently of each other. The 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:

$A$ bag contains $3$ red,$7$ white and $4$ black balls. If three balls are drawn from the bag,then the probability that all of them are of the same colour is

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is $P_1$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is $P_2$. Then:

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