Question

5 fill in the blank 20 points (a) a deli has a lunch special which consists of a sandwich, soup, and a dessert for $4.99. they offer the following choices: sandwich - chicken salad, turkey, ham, or roast beef soup - tomato, chicken noodle, or broccoli cheddar dessert - cookie or pie use a diagram to determine the number of different lunch combinations. then, use the fundamental counting principle to determine the number of different lunch combinations. type your answer.. (b) karl has 5 shirts, 3 pairs of pants, and 2 sweaters in his closet. how many different outfits that consist of a shirt, pair of pants, and sweater can he make? type your answer.. (c) if you roll a dice, then toss a coin, how many different outcomes could you get? type your answer.. (d) a license plate in canada consists of: letter, letter, letter, number, number, number. how many different license plates can be created? letters and numbers can be repeated. type your answer.. (e) a padlock has a 4 - digit combination using the digits 0 - 9. how many different padlock combinations are there if repetition of the numbers is allowed? type your answer..

Explanation:

Part (a)

Step1: Identify choices per category

Sandwich: 4 options (chicken salad, turkey, ham, roast beef)
Soup: 3 options (tomato, chicken noodle, broccoli cheddar)
Dessert: 2 options (cookie, pie)

Step2: Apply Fundamental Counting Principle

Multiply the number of options for each category: \( 4 \times 3 \times 2 \)

Step3: Calculate the product

\( 4 \times 3 = 12 \); \( 12 \times 2 = 24 \)

Step1: Identify choices per category

Shirts: 5 options
Pants: 3 options
Sweaters: 2 options

Step2: Apply Fundamental Counting Principle

Multiply the number of options: \( 5 \times 3 \times 2 \)

Step3: Calculate the product

\( 5 \times 3 = 15 \); \( 15 \times 2 = 30 \)

Step1: Identify outcomes per event

Dice roll: 6 outcomes (1–6)
Coin toss: 2 outcomes (heads, tails)

Step2: Apply Fundamental Counting Principle

Multiply the number of outcomes: \( 6 \times 2 \)

Step3: Calculate the product

\( 6 \times 2 = 12 \)

Answer:

24

Part (b)