#### Question

# Permutation, Combination, or Duplicates formula for this word problem?

A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many ways can you get 5 apples?

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Im stumped as to how to answer this question and I dont know which formula to use. I tried the duplicates formula, but my answer didnt match any of the answer choices.

If someone could please explain to me which formula to use and why, Id really appreciate it. Im trying to learn, not just get an answer, so Id rather emphasis be placed on the process rather than just giving me the answer. Best answer will be chosen on clarity and thoroughness. Thanks so much!

#### Answer

You'll have to use combination since the order isn't important.

so 6C5 = 6

there are 10 fruits in the bag....you can choose 5 fruits from 10 in 10C5 ways...but there r 6 apples...therefore favourable ways to choose 5 apples from them is 1(as the apples r identical .so you choose any set of 5 from 6 apples, the selection is same)...in any other way involving oranges you won't get 5 apples ...now if you look for the probability of getting 5 apples..then it's P(A) = 1/10C5

There are 6 apples and you are picking 5 so 6C5 = 6

There are 6 ways that you can pick 5 apples from 6 apples.

Not part of your question.

There are 10C5 or 252 total possible combinations

the probability of picking 5 apples=6/252 or 2.38%

There are 6 apples. How many ways can you choose 5 of them? That is 6C5, which equals 6. That assumes its even relevant which apples get chosen. If all apples are regarded as redundancies then there is only one way to choose five apples