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Can someone please tell me why 4x4x4=64 is not the right answer? There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.
Re: In how many ways can we put 4 different balls in 3 different boxes whe
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28 Sep 2016, 11:21
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
80 81 64 63 82
Answer: B.
Can someone please tell me why 4x4x4=64 is not the right answer? There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.
Kindly explain.
Thanks alot!!!
NOTE : The number of permutations/arrangments of n things , taken r at ta time when each item may be repeated once, twice...up to r times in any arrangement is \(n^r\) ways.
The first box can be filled in n ways, the second box can be filled in n ways(even though the first box is filled with one item, the same item can be used for filling the second box also because repetition is allowed), the third box can also be filled in n ways...
The rth box can be filled in n ways..
Now all the r boxes together can be filled in (n*n*n*....r times ) ie. \(n^r\) ways.
Re: In how many ways can we put 4 different balls in 3 different boxes whe
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28 Sep 2016, 15:23
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geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
80 81 64 63 82
Answer: B.
Can someone please tell me why 4x4x4=64 is not the right answer? There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.
Kindly explain.
Thanks alot!!!
"There are 4 ways to fill the 1st box" This assumes that the box needs to be filled. No requirement for any one box to contain ANY balls.
On the other hand, every ball needs to be placed somewhere. So, we need to examine the number of ways to place each ball. See my solution above.
Re: In how many ways can we put 4 different balls in 3 different boxes whe
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30 Dec 2018, 12:40
GMATPrepNow wrote:
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?
80 81 64 63 82
Answer: B.
Can someone please tell me why 4x4x4=64 is not the right answer? There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.
Kindly explain.
Thanks alot!!!
"There are 4 ways to fill the 1st box" This assumes that the box needs to be filled. No requirement for any one box to contain ANY balls.
On the other hand, every ball needs to be placed somewhere. So, we need to examine the number of ways to place each ball. See my solution above.
Cheers, Brent
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_________________
Thus the total number of ways in which 4 different balls can be put in 3 different boxes when any box can contain any number of balls is 3 x 3 x 3 x 3 = 81 _________________