Question

In a catalog, movies are identified by an ID number—2 letters followed by 3 digits.Repetitions are permitted. How many catalog numbers can be made?What is the probability that the ID number is divisible by 5? (Include the 2 letters in the ID number.)

Answer 1

Using the Fundamental Counting Theorem, it is found that:

• 676,000 catalog numbers can be made.

• There is a 0.2 = 20% probability that the ID number is divisible by 5.

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 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:

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

Hence the number of catalog numbers is:

$N = 26^2 \times 10^3 = 676000$

The ID number is divisible by 5 if the last digit is either 5 or 0, hence $n_5 = 0$ and the probability is:

$p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2$

There is a 0.2 = 20% probability that the ID number is divisible by 5.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

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