Lunch with Muhammad

Probability Level 4

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

This problem is posed by Muhammad A.

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