How many words can be formed by taking two identical and two distinct letters from the letters of the word $COMBINATION$?

$3$ boys $B_i, i = 1, 2, 3$ and $6$ girls $G_i, i = 1, 2, . . . , 6$ are to be seated in a row. The number of ways they can be seated so that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

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

In how many ways can $3n$ distinct objects be distributed equally among $3$ persons?

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

The number of ways of giving $20$ distinct oranges to $3$ children such that each child gets at least one orange is $............$.