Problem E

Three Items Only

Three-Item-Menu is a restaurant thats sells only hamburgers, french fries, and soft drinks.

One day, exactly \(120\) customers made a purchase. Half of the customers purchased at least a hamburger, \(\frac{1}{4}\) of the customers purchased at least french fries, but \(\frac{1}{3}\) of the customers purchased only a soft drink. Of the customers who bought a hamburger, \(\frac{4}{5}\) of them bought at least one other item.

How many customers purchased a hamburger and soft drink but not french fries?