If $^nP_5 = 9 \times ^{n-1}P_4$,then the value of $n$ is

If a man and his wife enter a bus in which five seats are vacant,then the number of different ways in which they can be seated is

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

How many groups can be selected for playing football out of $5$ ladies and $4$ gentlemen such that there should be one lady and one gentleman on each side?

Let $A = \{a_1, a_2, a_3, ..., a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

The number of ways to distribute $25$ apples among $4$ boys,such that each boy receives at least $4$ apples,is: