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avatarThonLibre2689
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Hello,i was genuinely curious about probability and found something in a shelf that could stack its accesory,i dont know really how to figure all of its possibles answers but i wanted to have help to understand better,so my question is: How many possible combinations are there for a collective hamburger toy with 4 toppings, 1 bottom bun that could be place anywhere however the cheese and the lettuce cannot be at last, and theres 1 bun that must always remains on top and have something to connected on?


thanks for if responded!

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      avatarLouis-Philippe Bteacher check
      Équipe Alloprof • 23h

      Thank you for your question!


      The hamburger has 1 topping bun that must be on the top, 1 bottom bun that can be anywhere, and 2 toppings that have to be somewhere in the middle. Let's build the hamburger from the bottom to the top :

      1. Bottom layer : there are 3 possible pieces (the lower bun, tomatoes, and patty)
      2. Second layer : 5 possible pieces, but one will always be used on the bottom, so 4 possible pieces
      3. Third layer : There are 5 possible pieces, but one will be used on the bottom and one on the second layer, so 3 possible pieces
      4. Fourth layer : There are 5 possible pieces, but one will be used on the bottom layer, on one the second layer, and one on the third layer, so 2 possible pieces
      5. Fifth layer : There are 6 possible pieces, but one will be used on the bottom layer, one on the second layer, one on the third layer, and one on the fourth layer, so 1 possible piece
      6. Sixth layer (top bun) : only 1 possible piece.


      The number of possible pieces can be found by multiplying all these possibilities :

      $$ n = 3 \times 4 \times 3 \times 2 \times 1 \times 1 $$


      There you go!


      This webpage explains permutations, arrangements, and combinations :

      https://www.alloprof.qc.ca/en/students/vl/mathematics/permutations-arrangements-and-combinations-m1346?draft=4a0b6a09-2813-4a71-9a16-507c8c699afa


      Don't hesitate if you need more help!

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