IIITH-PGEE

Question

how many way we can select 4 candies from 6 different groups?

Comments

Is it 6^4 (when order of selection is considered )or (6+4-1)C4 (when order of selection is not considered) ?

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n+r-1 Cr is used when things are identical but here 6 different groups are given

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you are right. but in these cases the characteristics depending on which we consider the objects as distinct or identical should not depend on the groups to which they are going to be assigned .

 

here candies are identical (I mean they are distinct by the groups they belong to otherwise if we don't consider their way of selection we can say they are identical)

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@shreya,if suppose we are given 6 different group of candies like (red,blue,grren,yellow,pink,orange).then how are they identical?

i am not sure about this.

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yes  candies are identical or not that should be mentioned also

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@Akriti just assume from our chosen 4 candies ,each of them can belong to any of the group depending on their color ,so r+b+y+g+p+o=4 : r no of candies belong to red group and so on , possible we have 3 red and 1 blue or 2 green 2 blue anything possible .. it is not like 4 distinct candies  whose colors are predetermined. so here we would say if they are identical or distinct not depending on their color but based on their order of selection ,if the candies are not numbered or distinguished by any other property we would say they are identical so (4+6-1)C4, but if order of selection matters ie. ist one to this color group ,2nd one to that color group then it should be 6^4.

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i did nt get you that whether candies are identical or not depends on their order of selection..:/

and u are saying that if order matters then it should be 6⁴.how so??because then we have 6 choices for each candy.

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@Srestha, d four candies in total or four candies from each group??

Also in a group it cud be dat d ones which r chosen cud b identical or distinct as well. Isn't it?

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@Akriti order will give numbering to the candies.  we choose ist from red 2nd from green 3rd from blue ,4 th from blue , and we choose 2 balls from blue and 1 from red and 1 from green in some other order is different. so 6 ^4 possibility ie ist one from any 6 colors(I mean group ) 2nd one from any 6 and this way for 3rd and 4th one too. but if order not to be considered then n+r-1 C r will be the answer.

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firstly,it is aking us to select the candies,so i dun think order matters here.

and secondly,i am not able to understand that how 6^4 will give you the order.:(

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so according to u what should be the answer?

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sorry..i wont be able to help.i am not good in PnC.

Answer 1

6^4 because for every candy we have 6 choices (Permutation,  Here order matters )

(6+4-1) C ₄ = 126  (Combination with repetition, Here order doesn't matter )