Three numbers are chosen at random from $1$ to $15$ . The probability that no two numbers are consecutive, is
$\frac{{11}}{{32}}$
$\frac{{44}}{{91}}$
$\frac{{33}}{{64}}$
$\frac{{22}}{{35}}$
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 fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-
All the spades are taken out from a pack of cards.From these cards, cards are drawn one by one without replacement till the ace of spade comes. The probability that the ace of spade comes in the $4^{th}$ draw 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
Two numbers $x$ $\&$ $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, ......, 1000\}$. Then the probability that $|x^4 - y^4|$ is divisible by $5$, is -