+102 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!
+128406 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
