If $^{n}P_{4} = 24 \times ^{n}C_{5}$,then the value of $n$ is

The last two digits of $2015! + 3^{2015}$ are:

$6$ different letters of an alphabet are given. Words with $4$ letters are formed from these given letters. The number of words which have at least one letter repeated and no two same letters are together is:

If the letters of the word $INTERMEDIATE$ are arranged,what is the probability that the two $E$'s do not come together?

Let $S = \{0, 1, 2, 3, \ldots, 100\}$. The number of ways of selecting $x, y \in S$ such that $x \neq y$ and $x + y = 100$ is

The domain of the function $f(x) = ^{16 - x}C_{2x - 1} + ^{20 - 3x}P_{4x - 5}$,where the symbols have their usual meanings,is the set