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

A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is

A dice marked with digit $\{1, 2, 2, 3, 3, 3\} ,$ thrown three times, then the probability of getting sum of number on face of dice is six, is equal to :-

A bag contains $3$ white and $7$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

Two marbles are drawn in succession from a box containing $10$ red, $30$ white, $20$ blue and $15$ orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

From a pack of playing cards three cards are drawn simultaneously. The probability that these are one king, one queen and one jack is