How to distribute the Candies?
The number of ways in which 6 distinct candies can be distributed between two girls such that each girl gets atleast one candy is?
The answer is 62.
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3 solutions
But that would have been the case had the candies been distinct. Here, they are specifically mentioned to be identical!
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Oops.. Sorry. i missed on that distinct part. yes, u r right. In this case, the solution would be C(n-1,r-1) which is C(5,1) = 5
The answer is 5 as the balls are identical...............
In this problem it is clearly written that the candies are identical not distinct...SO the number of ways they are distributed should be equal to the number of candies each girl can get and hence there are 5 possibilities (1,5),(2,4),(3,3),(4,2),(5,1).In other words it is the number of solutions of the equation x + y = 6 such that x >= 1 and y >=1.
The way the answer is presented saying each candy has two choices essentially assumes all the candies are DISTINCT!!That is girl 1 getting candy 1 is different from girl 2 getting candy 1 which clearly contradicts the statement the candies are identical.
So either this problem should be edited and our rating should be updated OR this problem should immediately be taken off the rating scale.
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I also entered 5 and got it wrong, I felt before answering that the question would be wrong because of its high rating contrary to its difficulty level. The staff should not have given it a rating. I don't get it why you reshared it.
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I reshared it so that more people can claim a dispute which will make it more likely for the staff to recover this problem...Otherwise many people can fall victim to this question
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@Eddie The Head – Thanks for your concern, submitting disputes is a good way to get our attention. I've updated the problem. For more information, you can read my comment on Vikesh's 'solution'.
Sorry............ maybe I should post it as a note with a warning........
Yeah, the staff should increase my rating😠😠😠😠😠😠
Exactly Eddie, I did the same. Did you send your solution in the 'request dispute' link given?
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Yes I did...I even shared a note requesting my followers to do the same....
This is a wrong question.Get your facts straight, Vikesh!
The answer is 5.
6 candies to be distributed between two girls.....
so give one to each , leaving us with 4 candies and satisfying condition in question
now to divide 4 among 2.
step 1: represent candy by "o" .......so we have "o" "o" "o" "o"
step 2 : add 1 "o" to above............so now we have "o" "o" "o" "o" "o"
step 3 : to divide candies into two, cancel out any "o" to make two partition/parts
step4: to do cancellation there are 5C1 ways = 5 ways.........hence answer is 5
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Worst! Lost my too many points! :(
the correct answer should have been 5,how can we get our points back?
There are two girls, and each must always get at least one candy. So there are 5 possible situations which we will consider individually (Girl 1 receives 5, 4, 3, 2, 1). There are 6 possible ways for Girl 1 to receive 5 candies (6 C 5 = 6). There are 15 possible ways for Girl 1 to receive 4 candies (6 C 4 = 15). Likewise, there are 6 possible ways for Girl 2 to receive 5 candies (situation where Girl 1 receives 1) and 15 possible ways for Girl 2 to receive 4 candies (situation where Girl 1 receives 2). So there are 42 distinct situations where the girls receive unequal amounts of candy (6 + 15 + 6 + 15). The final situation to consider is that in which each girl receives 3 candies. There are 20 possible ways for a girl to receive 3 candies (6 C 3 = 20). (The other girl must receive whichever 3 candies the first does not receive, so this does not add any possibilities). Therefore, there are 62 possible ways for the candy to be divided (42 + 20).
I apologise for the goof up.It arose due to a misunderstanding on my part and I didn't get chance to correct it due to some work commitments. The problem has been rectified. Sorry about the points which you guys lost. Would be careful in future.
This is the sequence of events.
1) The problem was created on March 20, with an answer of 62.
2) When I reviewed it, I asked
@Vikesh Koul
to clarify if the candies were identical or distinct. If they were distinct, then the answer of 62 would be correct.
3) Vikesh decided to state that the candies where identical.
4) Prior to today (4/21), only 1 dispute had been submitted. Vikesh didn't respond to the dispute.
5) Viskesh received several dispute today, and decided to update the question to state the the candies are distinct.
6) I noticed that several more disputes were submitted, and looked into the problem. I've marked those who answered 5 (as of 4/20) correct, and awarded points/ratings as such.
Consider all possible combinations. Each candy can be given to either of the two girls. So there are 2^6 ways of distributing them. Out of these combinations, there are 2 cases in which all the candies are given only to one girl. So the final result is 2^6 - 2 = 62