Probability of the same number in $4$ different groups is happen

Question

I have $4$ groups and each group can contain a decimal number range from $0000$ to $9999$. What is the probability that the four groups contain the same number, for example, the group $1$, group $2$, group $3$ and group $4$ have the number $0231$.

Answer 1

Well, the no. of ways of choosing a no. from the range is $^{10000}C_1$

So, probability that a certain number $x$ is present in all 4 groups is

$P=(\frac{1}{10000})(\frac{1}{10000})(\frac{1}{10000})(\frac{1}{10000})$

But, no. of ways of selecting $x$ is $^{10000}C_1$

So, net probability is

$P_0=^{10000}C_1 (\frac{1}{10000})(\frac{1}{10000})(\frac{1}{10000})(\frac{1}{10000})$

$\implies P_0=(\frac{1}{10000})^3$