Question

If there are $12$strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?

Short answer

The probability that no two of them celebrate their birthday in the

the same month is$\frac{12!}{{12}^{12}}$.

Step-by-step solution

Given Information.

There are $12$strangers in a room,

Explantion.

If $12$people are in the room:

The outcome space of the experiment is$S\left\{\left(x_1,x_2,x_3,\dots x_{12}\right):x_i\in \{1,2,3,\dots 12\}\right\}$ where the vector describes their months of birth.

because each element of the vector can be chosen inways.

As each outcome from the outcome space is equally likely, the Axioms give:

(is the number of elements in the set)

And the number of sample events in the event that no two people share their month of birth isthe number of different valued vectors insize.