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

A bag contains $3$ red, $4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

$3$ numbers are chosen from first $15$ natural numbers, then probability that the numbers are in arithmetic progression

Let $A$ denote the event that a $6 -$digit integer formed by $0,1,2,3,4,5,6$ without repetitions, be divisible by $3 .$ Then probability of event $A$ is equal to :

A five digit number is formed by writing the digits $1, 2, 3, 4, 5$ in a random order without repetitions. Then the probability that the number is divisible by $4$ is

The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-