Each of the persons $\mathrm{A}$ and $\mathrm{B}$ independently tosses three fair coins. The probability that both of them get the same number of heads is :

If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls 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

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads 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 -

The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :