Answer:
The answer is explained below
Step-by-step explanation:
A. How many ways can you distribute 4 different balls among 4 different boxes
The number of ways in which 4 different balls can be distributed among 4 different boxes is [tex]4^4=256\ ways[/tex]
B. How many ways can you distribute 4 identical balls among 4 identical boxes?
The number of ways in which 4 identical balls can be distributed among 4 identical boxes = P(4,1) + P(4,2) +P(4,3) + P(4,4) = 1 + 2 + 1 + 1 = 5 ways
Where P(k,n) is the number of partitions that k can be divided into n parts
P(4,1) = 4 = 1
P(4,2) = 1 + 3, 2+2 = 2
P(4,3) = 1 + 1 + 2 = 1
P(4,4) = 1 + 1 + 1 + 1 = 1
C. How many ways can you distribute 4 identical balls among 4 different boxes
The number of ways in which 4 identical balls can be distributed among 4 different boxes = [tex]C(4\ ball+4\ box-1,4\ box-1)=C(7,3)=\frac{7!}{(7-3)!3!}=35\ ways[/tex]
