# Thread: Classical definition of probability

1. ## Classical definition of probability

Two numbers $x$ and $y$ are chosen from the set $\{1,2,3.....,5n\}$. Find the probability that $x^4+y^4$ is divisible by $5$.

2. Hello,
Originally Posted by pankaj
Two numbers $x$ and $y$ are chosen from the set $\{1,2,3.....,5n\}$. Find the probability that $x^4+y^4$ is divisible by $5$.
Note that $(5k+r)^4$ with $r \in \{1,2,3,4\}$ has a remainder 1 in the division by 5.

Therefore, none of these numbers $5k+r$ would be such that $x^4+y^4$ is divisible by 5.

Remain the multiples of 5. There are n of them in the set. How many ways are there to choose 2 objects randomly among n ? (with replacement)