Question

A country with 7 seven regions has 7 festivals on February. Assume the festivals are located randomly, with all possibilities for which festival occurred where equally likely. What is the probability that some region had more than 1 festival on February? Explain all the steps you used, in order to find the solution.

Answer 1

The February in the problem has not much significance in counting the total and favorable ways. All tha matters in, what festial is celebrated in which region. Each of the 7 festivals has 7 possibilities to be celebrated in any of the regions. By fundamental rule of counting, first festival has 7 ways, second has 7 ways, and so on till seventh, so we multiply the ways to get toal ways for the festivals to be celebrated,

Now the number of ways to count the favorable ways directly is bit tedious. It would be almost impossible to count the ways in which some region had more than 1 festival on February. But the number of ways that each of the seven festival gets celebrated in a different region, is the number of ways to permute, i.e. arrange them one after the other. The first festival has 7 ways to be celebrated in any region, then the second festival has 6 choices, then the next one has 5 choices, etc. That is,

It is very highly likely, ~99.4% chance that some region had more than 1 festival on February