8 teachers and 4 students are sitting around a circular table at random, then the probability that no two students sit together is

A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability that exactly 5 of the balls in the bag are green is

In a binomial distribution the difference between the mean and standard deviation is 3 and the difference between their squares is 21 , then $P(x=1): P(x=2)=$

When an unfair dice is thrown the probability of getting a number $k$ on it is $P(X=k)=k^2 P$, where $k=1,2,3,4,5,6$ and $X$ is the random variable denoting a number on the dice, then the mean of X is