There are $n$ letters and $n$ addressed envelops. The probability that each letter takes place in right envelop is

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q- p$ is equal to

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r_1, r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $\omega^{I_1}+\omega^{\mathrm{I}_2}+\omega^{\mathrm{I}_3}=0$ is

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

Among $15$ players, $8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers