The Combinateria

Level pending

Harvey's school is offering a new menu in the cafeteria (above). Harvey doesn't like repetition, so he wants to eat a different combination of options every day. He can choose one or two sides, one drink, and one main course. However, he doesn't like 65 of the combinations and will not eat them. How many lunches will he be able to eat before he has to eat a combination he has eaten before?


The answer is 115.

Kaleil Salomon -Jacob by Kaleil Salomon -Jacob , 20, USA

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1 solution

There are 5 ! 3 ! 2 ! \frac{5!}{3!2!} or 10 combinations of 2 sides and 5 combinations of 1 side. The total number of lunch combinations is 15 (combinations of one or two sides) × \times 4 (drinks available) × \times 3 (main courses available). The total is 180. 180 - 65 = 115 \boxed{115}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

180 − ( 60 − 15 ) = 180 − 45 = 135 180 - (60 - 15) = 180 - 45 = \boxed {135}

You have gotta be kidding me.

Ralph Anthony Espos - 7 years, 3 months ago

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How do I fix it?

Kaleil Salomon -Jacob - 7 years, 3 months ago

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