You are home alone one day, and you are only left with a television, your computer and your fridge. While watching your favorite movie, you got hungry. You open the fridge and inside there are 5 Apples, 3 Bananas, and 4 Mangoes. You decide to have a snack that consists of 2 different fruits. In how many ways can arrange your snack?

Expert Answers

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You have 5 apples, 3 bananas, and 4 mangoes. You will eat two different fruits; in how many ways can you arrange your snack? Let A represent apple, B banana, and M mango.

There are multiple ways to solve this. Here is one:

Since there will be two different fruits we can find the number of ways for each possibility; for each possibility we use the fundamental counting principle:

(1) AB=5x3=15
(2) BA=3x5=15
(3) AM=5x4=20
(4) MA=4x5=20
(5) BM=3x4=12
(6) MB=4x3=12

Assuming the order you eat the fruit matters there are 94 different arrangements. (This is the number of permutations.)

If the order does not matter (e.g. banana then mango is essentially the same snack as mango then banana) then there are 47 different arrangements. (This would be the number of combinations.)

From the wording of the problem, I would select 94 different arrangements.


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