Lunch with Muhammad

A newly-opened restaurant has \( 5 \) menu items. If the first \( 4 \) customers each choose one menu item uniformly at random, the probability that the \( 4 \)th customer orders a previously unordered item is \( \frac{a}{b} \), where \( a \) and \( b \) are relatively prime positive integers. What is \( a+b \)?

This problem is posed by Muhammad A.

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