# It's $$V$$ versus $$X$$ and $$Y$$

Discrete Mathematics Level 3

Consider 2 numbers $$X$$ and $$Y$$ which are chosen at random from the set $$V=\{1,2,\ldots,3n\}$$ without replacement . If the probablity that $$X^{3}+Y^{3}$$ is divisible by 3 can be written of the form $\dfrac{n^{a}}{n^{b}+2^{c}},$

where $$a,b,c\in\mathbb{Z}$$ and $$n\in\mathbb{N}$$, find $$(a+c)\times b$$

If you feel that the probability cannot be expressed in this form then type 22 as your answer.

×