If three cards are drawn randomly from a pack of $52$ playing cards, then the probability of getting exactly one spade card, exactly one king, and exactly one card having a prime number 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 $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to

The probability that a randomly chosen $5-digit$ number is made from exactly two digits is

$A$ bag contains $3$ red,$4$ white,and $5$ black balls. If three balls are drawn at random,what is the probability that they are of different colors?

$A$ bag contains $12$ two-rupee coins,$7$ one-rupee coins,and $4$ fifty-paise coins. If three coins are selected at random,the probability that the sum of the values of the three coins is not an integral multiple of a rupee is: