SOLUTION: the homestyle cafe offers these combination in dinner menu * Meat item: Sikam pa, Chicken chili, Beef curry * Vegetables: peas, mushrooms * salads: fruits, fresh green *Dessert

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Question 1195817: the homestyle cafe offers these combination in dinner menu
* Meat item: Sikam pa, Chicken chili, Beef curry
* Vegetables: peas, mushrooms
* salads: fruits, fresh green
*Dessert: ice cream, cake.
if you choose one item from each category, how many days can you eat meals at the homestyle cafe before u eat the same dinner second time?

Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
.
the homestyle cafe offers these combination in dinner menu
* Meat item: Sikam pa, Chicken chili, Beef curry
* Vegetables: peas, mushrooms
* salads: fruits, fresh green
*Dessert: ice cream, cake.
if you choose one item from each category, how many days can you eat meals
at the homestyle cafe before u eat the same dinner second time?
~~~~~~~~~~~~~~~~~

You have 3 items in the 1st category  (meat);
         2 items in the 2nd category  (vegetables);
         2 items in the 3rd category  (salads);
         2 items in the 4-th category (dessert).


if you choose one item from each category,then, 
according to the Fundamental counting principle,
you may have 3*2*2*2 = 24 different dinners.


So, during 24 days, you may have different dinner.


So, 24 days you may eat different dinners, but on the day 25th you inevitably will eat the same dinner second time.


ANSWER.  At most, there are 24 days before you will eat the same dinner second time.

Solved and explained.

----------------

On Fundamental counting principle,  see the lesson
    - Fundamental counting principle problems
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



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