Find the number of ways of arranging $6$ red balls and $6$ black balls in a row such that no two black balls are together.

$60$ words can be made using all the letters of the word $BHBJO$,with or without meaning. If these words are written as in a dictionary,then the $50^{\text{th}}$ word is:

How many numbers between $5000$ and $10000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if no digit is repeated?

In a class of $20$ students,in how many ways can the following prizes be awarded?
If the first and second prizes are for Mathematics,the first and second prizes for Physics,the first prize for Chemistry,and the first prize for English are to be awarded.

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)