We want to see in how many ways we can divide 4 masks into 7 persons. We will see that the masks can be distributed in 35 different forms.
Notice that this is equivalent to seeing how many different groups of 4 friends we can take from the group of 7 persons.
Remember that if we have a set of N elements, the total number of groups of K elements that we can take from that set is:
[tex]c(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
We can use that formula with N = 7 and K = 4, so we get:
[tex]c(7, 4) = \frac{7!}{(7 - 4)!*4!} = \frac{7*6*5}{3*2} = 35[/tex]
So the masks can be distributed in 35 different forms.
If you want to learn more about combinations, you can read:
https://brainly.com/question/6779773
