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# Permutations/Combinations

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1. How many ways can you distribute \(4 \) different balls among \(4 \) different boxes?

2. How many ways can you distribute \(4 \) identical balls among \(4 \) identical boxes?

3. How many ways can you distribute \(4 \) identical balls among \(4 \) different boxes?

I need help. A hint or a solution is appreciated!

Feb 4, 2021
edited by AnxiousLlama  Feb 4, 2021

#1
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I'm  assuming  that we have no restrictions   ( some boxes can  be empty)

1.   k  distinct balls  into  n  distinct boxes =   n^k   = 4^4 =  256  ways

2. k indentical balls into n identical boxes   ....this one  is tough....it involves partitions.....as I'm going to  have to leave in a minute....I'll see if I can give you an answer later

3.   k identical balls into n distinct boxes  =  C (k +n - 1 , n-1) = C( 4 + 4  -1, 4 -1)  = C(7,4)   = 35 ways

C (7,4)   is the number of ways to  choose  4 things from 7  ....in case you are  not familiar with this  notation   Feb 4, 2021
#2
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BTW....here's a good  website  that explains some  of this  : https://journeywithdp.blogspot.com/2018/09/distributing-balls-into-boxes.html   Feb 4, 2021
#3
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this site also helps  https://journeywithdp.blogspot.com

Feb 4, 2021
#4
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Got it. Thank you so much guys!

Feb 4, 2021