The total number of selections of the letters in the phrase "ned needs nineteen nets" is:

The difference between an integer $n$ and its cube $n^3$ is always divisible by which of the following?

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

For a natural number $n$,the inequality $2^n(n - 1)! < n^n$ holds true if:

There are $n$ white and $n$ black balls marked $1, 2, 3, \ldots, n$. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

Assuming that the balls of the same color are identical,find the number of ways to select one or more balls from $10$ white,$9$ green,and $7$ black balls.