Tricky Customer

Charlie doesn't want his new house number to be divisible by 3 or 5. How many choices of house does he have?
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Problem



Charlie wants to buy a new house but he doesn't like house numbers that are divisible by $3$ or by $5$.

If all the houses numbered between $100$ and $150$ inclusive are for sale, how many houses can he choose from?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.