SOLUTION: How many ways are there to place 4 distinct balls into 5 distinct boxes such that exactly 3 of the 5 boxes do not have any balls?

Algebra.Com
Question 1129916: How many ways are there to place 4 distinct balls into 5 distinct boxes such that exactly 3 of the 5 boxes do not have any balls?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
How many ways are there to place 4 distinct balls into 5 distinct boxes such that exactly 3 of the 5 boxes do not have any balls?
# of ways to pick the two boxes to receive balls:: 5C2 = (5*4)/(1*2) = 10 ways
-----
# of ways to lace 4 distinct balls in those 2 distinct boxes::
(# in box A, # in Box B)
(0,4) 1 way
(1,3) 4 ways
(2,2) 6 ways
(3,1) 4 ways
(4,0) 1 way
Total (A,B) ways:: 16
------
Final Answer:: 10*16 = 160
--------------------------
Cheers,
Stan H.
----------

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
In this problem, the order of 2 selected boxes is important and does matter.


Therefore, we have 5*4 = 20 different box arrangements - not 10 combinations, as @stanbon uses.


Then the total number of ways is 20*16 = 320 - not 160.


The correct answer is 320 ways.


RELATED QUESTIONS

How many ways are there to distribute 15 district objects into 5 distinct boxes with: i) (answered by greenestamps)
How many ways are there to distribute 15 district item into 5 distinct boxes with:... (answered by Edwin McCravy,greenestamps,ikleyn,rippletable)
may you please help with this question: There are four boxes in a line.In how many ways... (answered by rothauserc)
How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable... (answered by josmiceli)
How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable... (answered by math_helper)
How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but... (answered by math_helper)
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)
b) How many ways are there to distribute 20 district object into 10 distinct boxes with (answered by stanbon)
How many ways are there to distribute 20 district object into 10 distinct boxes with... (answered by robertb)