Combinatorics: 10 light bulbs of which 3 are broken. Q.How many ways can you pick...?

NoGodButAllah

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Mar 10, 2017
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There are 10 light bulbs at which 3 are broken.
Q.How many ways can you get 4 light bulbs.
A.7C4 or 10C4
Q.How many ways can you get 4 light bulbs, with 2 working and 2 not working.
A.3C2*7C2

Could you guys tell me if I did it correctly? Thanks

Sorry my wording was off.
 
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I agree with your answer to the second question, but I don't agree with your answer to the first. "How many ways can you pick the fourth light bulb?" is a bit confusing to me. Let's say we arbitrarily numbers the bulbs. One of the bulbs will be "the fourth" but we have no way of knowing if it will be one of the broken ones or one of the functioning ones. Taking the question at face value, we'd then be tasked with finding all pairing of four numbers from 1 to 10, where one of the numbers is 4. So there's 1234, 1254, 1264, etc. Then it's also a question of does order matter? Is the pairing 4321 different from 2134?
 
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