The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students,four are swimmers is

Let a random variable $X$ have a Binomial distribution with mean $8$ and variance $4$. If $P(X \leqslant 2) = \frac{k}{2^{16}}$,then $k$ is equal to:

If the mean and variance of a binomial variate $X$ are $\frac{4}{3}$ and $\frac{8}{9}$ respectively,then $P(X=2)=$

If the mean and variance of a binomial distribution are $4$ and $\frac{4}{3}$ respectively, then $P(X=2)=$

In an examination,there are $10$ true-false type questions. Out of $10$,a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k}{4^{10}}$,then $k$ is equal to

Find the binomial probability distribution whose mean is $3$ and variance is $2$.