A $15 \mathrm{cm}$ coloured cube is cut into $3 \mathrm{cm}$ small cubes then how many cubes are formed which have only one face painted.

If we throw a dice, what is the probability of obtaining a result that is less than $4$. If we know that the result obtained was an even number?        

There are $10$ balls in a box, $5$ white and $5$ black. Two balls are removed randomly from the box, one after another. The first ball that is removed is black and it is not returned to the box. What is the probability that the second ball that is removed is also black? 

Find the value of ${\mathrm{x}}^3+{\mathrm{y}}^3+{\mathrm{z}}^3-3\mathrm{xyz}$. If $\mathrm{x}+\mathrm{y}+\mathrm{z}=15$ and ${\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2=51$  

In a class composed of $x$ girls, $y$ boys. What part of the class is composed of girls?      

The expression $2^{6\mathrm{n}}-4^{2\mathrm{n}}$, where $\mathrm{n}$ is a natural number is always divisible by