In how many ways can 5 different fruits be distributed among four children? (Some children may get more than one fruit and some may get no fruits.)
(A) 4^5
(B) 5^4
(C) 5!
(D) 4!
(E) 4!*5!
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(A) 4^5
(B) 5^4
(C) 5!
(D) 4!
(E) 4!*5!
[Reveal] Spoiler:
Correct Answer is 1024 and I understand the reasoning behind that.
But the approach I followed was:
Say we keep the 5th fruit aside and distribute the other 4 fruits among the 4 children
No of ways to distribute 4 fruits among 4 children = 4!
Now for each of these 4! Combinations, 5th fruit can be distributed to any of the 4 children
i.e. 4 new combinations for each of the 4! combinations
No of ways to distribute 5th fruit = 4*4!
5th fruit can be selected in 5 different ways
Total combinations are 5*4*4! = 480
Whats wrong here? What is it that I am missing here? What are the other 1024-480 combinations that I am missing?
But the approach I followed was:
Say we keep the 5th fruit aside and distribute the other 4 fruits among the 4 children
No of ways to distribute 4 fruits among 4 children = 4!
Now for each of these 4! Combinations, 5th fruit can be distributed to any of the 4 children
i.e. 4 new combinations for each of the 4! combinations
No of ways to distribute 5th fruit = 4*4!
5th fruit can be selected in 5 different ways
Total combinations are 5*4*4! = 480
Whats wrong here? What is it that I am missing here? What are the other 1024-480 combinations that I am missing?