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question: When 4 coins are tossed simultaneously, two of them are 1 cent (indistinguishable) and the other two are 5 cents (indistinguishable). a) What are the possible results that can be obtained? b) How many cases are there in which 2 heads and 2 tails come up?

i try do this: do 2 subsets one with two of them are 1 cent and the other are 5 cents maybe could be but here i get lost xd i need help please

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    $\begingroup$ Ignore the nickels for now and focus on the pennies. With two pennies you have the possibility that you have two heads, or you have one head and one tail, or you have two tails. Since the pennies are indistinguishable you can not tell the difference between getting one head and one tail from the outcome where you got one tail and one head. Warning: Do not make the mistake of thinking that these three outcomes are equally likely to occur. They are not. $\endgroup$
    – JMoravitz
    Oct 27, 2020 at 21:20
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    $\begingroup$ Now, the nickels are similar. To have both accounted for simultaneously, just apply rule of product. $\endgroup$
    – JMoravitz
    Oct 27, 2020 at 21:21

1 Answer 1

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a) For each type of coin (pennies and nickels), there are three distinguishable results ($2H$, $1H$ $1T$, $2T$). Since there are two distinguishable types of coins, there are $3\cdot3=\boxed{9}$ total distinguishable results that can be obtained.

b) Assuming that for this part, a "case" still counts as a distinguishable result, we know that in order to get $2H$ and $2T$, either one type of coin is $2H$ and the other type is $2T$ (2 distinguishable cases), or each type of coin results in $1H$ and $1T$ (1 distinguishable case). So the answer to this problem is $\boxed{3}$.

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