Question
58 b and c
How many ways are there to put six temporary into four identical offices so that there is at least one temporary employee in each of these four offices? How many ways are there to distribute five indistinguishable object into three indistinguishable boxes? How many ways are there to distribute six indistinguishable objects into four indistinguishable boxes so that each of the boxes contains at least one object? How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD? How many ways are there to pack nine identical DVDS into three indistinguishable boxes so that each box contains at least two DVDs? How many ways are there to distribute five balls into seven boxes if each box must have at most one ball in it if a) both the balls and boxes are labeled? b) the balls are labeled, but the boxes are unlabeled? c) the bails are unlabeled, but the boxes are labeled? d) both the balls and boxes the unlabeled? How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if a) both the balls and boxes are labeled? b) the balls are labeled, but the boxes are unlabeled?
Explanation / Answer
Dear Student Thank you for uisng Chegg !! Given that there are 5 balls and 7 boxes, No of ways to distribute at most 1 b) Balls are labelled but boxes are unlabelled Now since each box can contain a maxium of 1 ball And all the boxes are identical => There is only 1 way to put 5 balls into 7 boxes with atmost 1 ball in each box c) Balls are unlabelled but boxes are labelled In this case we need to select 5 out of 7 distinct boxes where ball is put No of ways of selection of 5 boxes out of 7 is 7C5 = 21 No of ways of distribution is 1 Total Number of ways = 21 * 1 = 21 Solution
