If $7$ dice are thrown simultaneously,then the probability that all six digits appear on the upper faces is equal to -

Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

If a $3$-digit number is randomly chosen,what is the probability that either the number itself or some permutation of the number (which is a $3$-digit number) is divisible by $4$ and $5$?

$A$ die is rolled three times. The probability of getting their sum equal to a prime number of the form $4n+1$ is

In a game, two dice are thrown simultaneously by a person $A$ and two cards are drawn at random simultaneously from a pack of $52$ playing cards by a person $B$. They win the game if $A$ gets a prime score as the sum of the numbers appearing on both the dice and $B$ gets a face card and a card having a prime number. Then the probability that both $A$ and $B$ win is: