Question

A lottery game requires a person to select two upper case letters and three differentnon-zero digits. How many choices can the customer make? You may leave your answer as aproduct.

Answer 1

Answer:

26²×9×8×7

Step-by-step explanation:

To select one ticket from the lottery, the costumer has to make five individual choices, the two letters and the three non-zero digits. To choose the first letter, the person can take any of the 26 letters of the english alphabet. In the same way, the person has 26 choices for the second letter (repetition doesn't matter in this problem).

For the first digit, the costumer has 9 choices. The second digit must be different from the first one, so it has 8 possibilities, and the third digit has 7 choices (it must be different from the previous two).

Using the product rule, the number of ways of choosing the five symbols is 26×26×9×8×7=26²×9×8×7.