The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

There are $(n + 1)$ white balls and $(n + 1)$ black balls. Each ball is numbered from $1$ to $(n + 1)$. In how many ways can these balls be arranged in a row such that no two balls of the same color are adjacent?

The number of ways of selecting $8$ letters from $24$ letters,of which $8$ are $a$,$8$ are $b$,and the remaining $8$ are distinct,is given by:

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is