Q: Find how many integers $n$ satisfying $ 1\le n \le 5000$ are divisible by at least one of the numbers 4, 7 and 33.
I've done the following:
$|A| = \lfloor 5000/4 \rfloor = 1,250 $ $|B| = \lfloor 5000/7 \rfloor = 714 $ $|C| = \lfloor 5000/33 \rfloor = 151 $
$|A\cap B| = \lfloor 5000/(4 * 7) \rfloor = 178$ $|A\cap C| = \lfloor 5000/(4 * 33) \rfloor = 37$ $|B\cap C| = \lfloor 5000/(7 * 33) \rfloor = 21$ $|A \cap B\cap C| = \lfloor 5000/(4 * 7 * 33) \rfloor = 5$
Next I do this:
$|A|+|B|+|C| - |A\cap B| - |A\cap C| - |B\cap C| + |A \cap B\cap C|$
Which works out as:
$1,250 + 714 + 151 - 178 - 37 - 21 + 5 = 1,884$
Answer = 1,884.
Is this correct?