Answer:
3876
Step-by-step explanation:
We have the following data:
Members of the fraternity = 20
Their attendance at five parties is organized into groups of four.
This indicates that each group consists of 4 individuals.
At least one brother will be present at exactly one of the gatherings. (The brothers are indistinguishable).
Thus, precisely one brother at a gathering leaves (20 - 1) = 19, due to their indistinct nature.
Group sizes are in fours.
Calculating 19C4:
From: nCr = n! /(n-r)! r!
19C4 = 19! / (19 - 4)! 4!
= 19! / 15! 4!
= (19 * 18 * 17 * 16) / (4 * 3 * 2)
= 93024 / 24
= 3876