4. How many different ways can you put 8 balls in 8 boxes A1, . ....

80.2K

Verified Solution

Question

Statistics

4. How many different ways can you put 8 balls in 8 boxes A1, .. . , A8
if (a) the balls are all different and no box is empty 8!
(b) the balls are all different and only three boxes A1, A2 andA3 are empty
(c) the balls are all different and exactly four boxes areempty
(d) the balls are all different and each box is either empty orcontains exactly two balls
(e) the balls are identical
(f) the balls are identical and exactly two boxes are empty
please explain in detail too thanks! especially e and f

Answer & Explanation Solved by verified expert

4.2 Ratings (533 Votes)

We have 8 balls with us and we want to put them in 8 boxesA1 A2A8 under the followingdifferent situationsParta The balls are different and no box isemptySince we have 8 balls and none of the boxes are to be emptyeach of the boxes will have only one ballSo let us start by filling the box A1 then go onfilling the boxes A2 A3 and lastlyA8Let us now fill the box A1 We can put any one of the8 balls in that box Since the 8 balls are different this can bedone in 8 ways So in any one of the 8 ways we put one ball inthat boxHaving put one ball in box A1 we have 7 balls athand one of which needs to be put in the box A2 Herewe note that for any one ball put in the box A1 in 8ways any one of the remaining 7 balls can be put in the boxA2 in 7 ways So we can fill the boxes A1and A2 with two balls in 87 waysNow having put two balls in boxes A1 andA2 we have 6 balls at hand one of which needs to beput in the box A3 Herewe note that for any two balls put in the boxes A1 andA2 in 87 ways any one of the remaining 6 balls can beput in the box A3 in 6 ways See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member