Using the Fundamental Counting Theorem, we have that:
4. 1,757,600 different license plates can be there.
5. 676,000,000 different driver's license numbers can be formed.
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]
For the letters there are 26 outcomes and for the digits there are 10 outcomes, hence the parameters for item 4 are given as follows:
[tex]n_1 = n_2 = 26, n_3 = n_4 = 10, n_5 = 26[/tex]
Hence the number of license plates is given by:
N = 26 x 26 x 10 x 10 x 26 = 1,757,600.
For item 5, the parameters are:
[tex]n_1 = n_2 = 26, n_3 = n_4 = n_5 = n_6 = n_7 = n_8 = 10[/tex]
Hence the number of license numbers is:
26 x 26 x 10 x 10 x 10 x 10 x 10 x 10 = 676,000,000
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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