Birthday paradox, with a twist!

A common mistake is that each person should have a prob. of $\frac{1}{365}$ to have their birthday on a specific date. That means $5000$ people should have that prob. to the power of $5000$ ! That is wrong though!

The correct answer is B. Think of it as this:

What is the probability that 3 people have their birthday on the same date in 1 week ? (Mon - Sun)

The answer of it would be $\frac{1}{49}$ as for 2 people, the prob. is $\frac{1}{7}$ , or $\frac{7}{49}$ and 3 people are just $\frac{7}{7^3}$ , or $\frac{1}{49}$ !