Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:
n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.
Thus the number of ways is:
N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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