Question

Help please

Answer 1

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.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

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:

$n_1 = n_2 = 26, n_3 = n_4 = 10, n_5 = 26$

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:

$n_1 = n_2 = 26, n_3 = n_4 = n_5 = n_6 = n_7 = n_8 = 10$

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 brainly.com/question/24314866

#SPJ1