# Waiting For The Bathroom

Discrete Mathematics Level 5

Carla is attending a concert and she has to use the bathroom. Unfortunately, the concert venue has only one Porta-Potty! There are 10 people in line, and each person in line takes either 1, 2, 3, 4, or 5 minutes to go to the bathroom. If Carla had to wait 35 minutes to use the bathroom, how many possible ways could the people ahead of her have used the bathroom? In other words, how many ways can we fill a multiset of 10 elements with the numbers 1, 2, 3, 4, and 5 such that their sum is 35?

Details and Assumptions

• For example, People 1 through 5 could all have used the bathroom for 3 minutes, while People 6 through 10 could each have used it for 4 minutes. $$5\times3+5\times4=35$$, therefore this is one of the possible lines that Carla could have waited in.

• Carla gets in line the moment that Person 1 begins to use the Porta-Potty.

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