1. A plate number is made up of three letters from the English alphabet followed by a
three-digit number. How many plate numbers are possible if:
a. the letters and digits can be repeated in the same plate number?
b. the letters and digits cannot be repeated in the same plate number?
2. You have a choice of one main dish, one vegetable, and one beverage. The ma
dish choices are lobster, chicken, fish or steak. The vegetable choices a
ampalaya, lettuce or broccoli. The beverage choices are soda, tea or pineapple.
a. How many outcomes show lobster?
b. How many outcomes show chicken and broccoli?
c. How many dinners are possible?

Question

02-05-2024
Mathematics

Answered

1. A plate number is made up of three letters from the English alphabet followed by a
three-digit number. How many plate numbers are possible if:
a. the letters and digits can be repeated in the same plate number?
b. the letters and digits cannot be repeated in the same plate number?
2. You have a choice of one main dish, one vegetable, and one beverage. The ma
dish choices are lobster, chicken, fish or steak. The vegetable choices a
ampalaya, lettuce or broccoli. The beverage choices are soda, tea or pineapple.
a. How many outcomes show lobster?
b. How many outcomes show chicken and broccoli?
c. How many dinners are possible?

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-05-02T17:44:07-04:00

1. For the plate number scenario: a. When the letters and digits can be repeated, you have 26 choices for each letter (A-Z) and 10 choices for each digit (0-9). Therefore, the total number of plate numbers possible is calculated by multiplying the number of choices for each component: 26 choices × 26 choices × 26 choices × 10 choices × 10 choices × 10 choices. b. When the letters and digits cannot be repeated, the calculations change. For the first letter, you have 26 choices, for the second letter 25 choices (since you can't repeat the first letter), and for the third letter 24 choices. Similarly, for the first digit, you have 10 choices, for the second digit 9 choices, and for the third digit 8 choices. To find the total number of plate numbers possible without repetition, you multiply the number of choices for each component: 26 choices × 25 choices × 24 choices × 10 choices × 9 choices × 8 choices. 2. For the dinner scenario: a. To determine the number of outcomes that include lobster as the main dish, you consider that there are 4 main dish choices, 3 vegetable choices, and 3 beverage choices. Therefore, the total number of outcomes showing lobster is calculated by multiplying the choices for each component: 1 choice for lobster × 3 choices for vegetable × 3 choices for beverage. b. To find the number of outcomes showing chicken and broccoli, you have 1 choice for chicken, 1 choice for broccoli, and 3 choices for beverage. Therefore, the total number of outcomes with chicken and broccoli is calculated by multiplying the choices for each component: 1 choice for chicken × 1 choice for broccoli × 3 choices for beverage. c. The total number of possible dinners can be found by multiplying the number of choices for each category: 4 choices for the main dish × 3 choices for the vegetable × 3 choices for the beverage. This will give you the total number of different dinner combinations possible.