Hint
As we don't know how of the people were library members, you can try a random number and see what happens.
Answer
4,200 books.
Reasoning
It doesn't matter how many library members there were, as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly, it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
Double-Checking
Both the members and non-members accepted, on average, 3 books each.
Hint
There are 3 P's, so there are 3 different ways to start the word.
Answer
960.
Reasoning
Given: P P P U U Z Z Z Z Z L L L L E S S.
The order of the Z's is important. For example, we could chose a red one and a green one, so the order they appear in the sign has to be taken into consideration.
There are:
3 different P's that could be chosen.
2 different U's that could be chosen.
5 different Z's that could be chosen.
4 different Z's that could be chosen, as one has already been chosen.
4 different L's that could be chosen.
1 E that could be chosen.
2 different S's that could be chosen.
So there are 3 x 2 x 5 x 4 x 4 x 1 x 2 = 960 different ways to make the sign.
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