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

$^{n - 1}C_r = (k^2 - 3) \cdot ^nC_{r + 1}$ if $k \in$

There are $(n + 1)$ white and $(n + 1)$ black balls,each set numbered $1$ to $(n + 1)$. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colours is

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits so that the odd digits occupy even places?

The number of ways in which ten candidates $A_1, A_2, ....... A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is

In an examination,there are three multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is: