Question

A lottery game requires that a person select in uppercase or lowercase letter followed by two different two-digit numbers (where the digits cannot both be zero). How many different ways are there to fill out a lottery ticket

Answer 1

Using the Fundamental Counting Theorem, it is found that there are 416,520 ways to fill out a lottery ticket.

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:

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

In this problem:

• First, one uppercase or lowercase letter is chosen, there are 26 of each, hence $n_1 = 52$.

• Then, two different two-digit numbers are chosen, and there are 90 of them, hence $n_2 = 90, n_3 = 89$, as the third digit has to be different of the second.

Then:

$N = n_1n_2n_3 = 52(90)(89) = 416520$

There are 416,520 ways to fill out a lottery ticket.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866