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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align} & \normalsize \text{Their are 4 apples, 5 mangoes and 6 watermelons .}\hspace{.33em}\\~\\ & \normalsize \text{Find the number of ways }\hspace{.33em}\\~\\ & \normalsize \text{i.) I can purchase at least each of them. }\hspace{.33em}\\~\\ & \normalsize \text{ii.) I can purchase at least one of them. }\hspace{.33em}\\~\\ \end{align}}\)
notice that apples have 5 states : {0, 1, 2, 3, 4} mangoes have 6 states : {0, 1, 2, 3, 4, 5} watermelons have 7 states : {0, 1, 2, 3, 4, 5, 6}
yes

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is this correct =(2^4-1)*(2^5-1)*(2^6-1)
I believe so
the english is a bit unclear to me " I can purchase at least each of them"
but it is given 4*5*6 ways
in book
thats the answer for part a) ?
yes
for partb, is the answer 5*6*7 - 1 ?
yes for part b
it seems textbook is treating all the fruit types as indistinguishable @jayzdd
yes , hmm i guess i treated them as distinguishable
all apples are are identical and so all mango
For the apple choice you can pick 1 apple 2 apples 3 apples 4 apples a total of 4 ways to select the apples Then multiply this by the number of selections you can make for mango 1 mango 2 mangoes 3 mangoes 4 mongoes 5 mangoes a total of 5 choices and then similarly for the watermelon there are 6 ways to select them by multiplication principle, 4*5*6
ok
for part b) now include the zero case
For the apple choice you can pick 0 apples, 1 apple, 2 apples, 3 apples , 4 apples a total of 5 ways to select the apples Then multiply this by the number of selections you can make for mango 0 mango 1 mango 2 mangoes 3 mangoes 4 mangoes 5 mangoes a total of 6 ways to select And then similarly for the watermelon 0 watermelon, 1 watermelon, ... 6 watermelon there are 7 ways to select them By multiplication principle, 5*6*7 But the directions say at least one fruit, so we cannot have 0 apple and 0 mangoe, and 0 watermelon. so we subtract 1
like these method in the previuos question there were 5 methods for bulb so how can i judge distinguishable bulbs or fruits
The bulbs were fixed by the socket, so there was an ordering to them. lightbulb 1, lightbulb2, ... lightbulb 5 Here there is no natural order to the fruits, since they are indistinguishable. If they want to treat the fruits as distinguishable, the directions would explicitly say it. otherwise assume indistinguishable
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the sockets are distinguishable i would say , and there are 2 states for each socket (on or off)
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If the lightbulbs had no sockets, then the lightbulbs would be indistinguishable. But then there would be no light either. Since lightbulbs had light, we could assume they were connected to distinguishable sockets, and cannot move. This forces an ordering to the lightbulbs that make them distinguishable.
The lightbulbs connected to the sockets are fixed in space and bolted down, because they are constructed that way by the carpenter. But the apples and mangoe fruits are not bolted down, so what matters is how many you pick, not which one
Think of it this way. When you select the fruits, imagine you are blindfolded. There are three bags, a bag for apples , a bag for mangoes, bag for watermelons. You are instructed to select as many fruits from each bag as you want. The apples are all the same (let's imagine for the sake of argument). The mangoes are all exactly the same and the watermelons the same. you can select 0 apples, 1 apple, 2 apples... up to 4 apples. you can select 0 mangoes up to 5 mangoes, etc Doing this blindfold experiment would not make sense for the lighbulb example.
sry was afk

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