Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{ k }{2^{15}}$, then $k$ is equal to:

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is

Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialled at random. The probability that the number is dialled correctly, is

A bag contains $5$ distinct Red, $4$ distinct Green and $3$ distinct Black balls. Balls are drawn one by one without replacement,then the probability of getting a particular red ball in fourth draw is-

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$, is

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