Here is the question.
Each of the 90 students participated in at least one of the three track events A, B and C. If 20 students participated in A, 40 students participated in B, and 60 students participated in C, and if 5 students participated in all three events, how many students participated in at least two of these events?
Now, I applied the simple inclusion exclusion principle here -
$|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C| \\ |A \cap B| + |A \cap C| + |B \cap C| = |A| + |B| + |C| + |A \cap B \cap C| - |A \cup B \cup C|$
This gives 35 as the result. However the current result is 20 (as per attached explanation). What am I doing wrong here?