Two dice are thrown  $5$ times, and each time the sum of the numbers obtained being  $5$ is considered a success. If the probability of having at least $4$ successes is $\frac{\mathrm{k}}{3^{11}}$, then $\mathrm{k}$ is equal to

A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ memiers) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Words with or without meaning are to be formed using all the letters of the word $EXAMINATION.$ The probability that the letter $\mathrm{M}$ appears at the fourth position in any such word is:

A committee of two persons is selected from two men and two women. What is the probability that the committee will have  one man ?

A box contains $10$ red balls and $15$ green balls. If two balls are drawn in succession then the probability that one is red and other is green, is

A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then the probability that $2$ are white and $1$ is red, is