SOLUTION: How many ways can three indistinguishable dots be arranged in five different boxes? Ex: [*][*][*][ ][ ] Swapping one dot with another will make no difference, as all the dots

Algebra.Com
Question 1076953: How many ways can three indistinguishable dots be arranged in five different boxes?
Ex: [*][*][*][ ][ ]
Swapping one dot with another will make no difference, as all the dots are indistinguishable.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
How many ways can three indistinguishable dots be arranged in five different boxes?
Ex: [*][*][*][ ][ ]
Swapping one dot with another will make no difference, as all the dots are indistinguishable.
~~~~~~~~~~~~~~~~ 

1.  There are 5 ways to put 3 dots into ONE of 5 boxes.


2.  There are 5*4 = 20 ways to put 2 dots in one of 5 boxes and 1 dot to one of 4 remaining boxes.


3.  There are  = 10 ways to put 3 dots into 5 boxes keeping no more than 1 dot in each box.


4. In all, it gives 5 + 20 + 10 = 35 for the number under the question.


RELATED QUESTIONS

in how many ways can five dashes and eight dots be... (answered by galactus)
In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable (answered by greenestamps)
In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable (answered by ikleyn)
Out of 26 letters, In how different many ways of five digit can be... (answered by Edwin McCravy)
In how many ways can you distribute $8$ indistinguishable balls among $6$ distinguishable (answered by ikleyn,Edwin McCravy)
In how many ways can 5 balls be placed in 4 boxes, if 2 balls are white and 3 balls are... (answered by CPhill,mccravyedwin,Edwin McCravy)
Five boxes are to be arranged on a shelf, but there is only enough space for three books. (answered by jim_thompson5910)
in how many different ways can the symbols *, #, ^ , & , ! be... (answered by jim_thompson5910)
In how many different ways can 4 stamps be... (answered by ewatrrr)