Probability that at least 2 people chose the same number

Question

Each person in a group of n people is requested to select a whole number between 1 to k. Describe the probability that at least 2 people chose the same number.

My answer was
$P(x)=favorable\ cases / posible\ cases$
$P(x) = C_2^nC_{n-2}^K\ /\ Vr_{K}^n$

But the teacher told me it was wrong. What am I not seeing?

Answer 1

For $k\ge n$, it's just 1- the probability that everyone chooses different numbers.

$1-\displaystyle \frac{k*(k-1)*...*(k-n+1)}{k^n}$