Let\'s put balls into boxes! We have 5 distinct boxes and an unlimited supply of
ID: 3224695 • Letter: L
Question
Let's put balls into boxes! We have 5 distinct boxes and an unlimited supply of balls of 12 different kinds. (a) How many ways are there to put just 10 balls into the 5 boxes if you can't use more than a single ball of any kind? (b) How many ways are there to put 10 balls into the 5 boxes if you are supposed to use only one kind of ball? (c) How many ways are there to put 10 balls into a single, lone box if you may use a mixture of different kinds of balls? (d) How many ways are .here to put 10 balls into 5 boxes if either you only use one kind of ball or you put exactly two balls in each box.Explanation / Answer
A.1 Total boxes=5
Total balls (of kinds)=12
no of ways=12P10
=12!/2!
=12*11*10*….*3
no of ways=239500800
A.2) as we have 12 types of balls and only single ball to be used in all the boxes
therefore, there are a total of 12 ways
A.3) we need to use mixture of balls
no of ways the 10 balls can be chosen out of 12 kinds is 12^10 ways
as we have to use mixture of balls, the outcome of same ball used 10 times to be removed
hence , the total number of ways are 12^10-12 ways
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