In how many ways can 5 chocolates be chosen from an unlimited number of Cadbury,Five-star, and Perk chocolates?

Question

we have to choose five chocolates,say, C1, C2, C3, C4 and C5. Now for C1 we can choose among three kinds of chocolates. Since the supply of chocolates is infinite, for C2, again we Can choose among three kinds of chocolates. Similarly for each of C3, C4, C5, we have three options. So total number of choices =3^5=243.

Now if we have a case like CCCCP and PCCCC , so then these cases are counted distinct but they should be same , so then how to proceed from here ?

Comments

yes, they are not identical- and they correspond to the 3 distinct bins. But our balls here are just selections- we select 5  chocolates and correspondingly put 5 balls among the 3 bins corresponding to the 3 types of chocolates.

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Sir , actually I couldn't get how are we considering the chocolates to be identical ,"our balls here are just selections" what does this signify ? Does it have no effect on whether the object is identical or distinct ?

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Actually we have to reduce the problem here. Consider like 5 identical chocolates (balls) and 3 distinct bins for 5-star, perk and cadbury respectively. If a chocolate goes to bin for perk, it becomes a perk and so on for other two also.

Answer 1

C |F |P

*** |** |   HERE it means 3 CADBOURY ....2FIVE STAR and 0 PERKS ...same like that u can 

divide 5 stars in any partitions .SO 7C2 is the answer ....and by formula too ..(5+3-1)C(3-1)

Comments

I referred this link and got my solution but I couldn't get your logic , how you did (5+3-1)C(3-1)  ?

http://mathforum.org/library/drmath/view/68607.html

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3-1 are no. of dividers, 5 is no. of stars.