Math / Algebra

QuestionEthan is at a sandwich shop and is looking at the combo meal, which includes a sandwich, a choice of 2 sides, and a medium drink. He has to decide between 5 different sandwiches, 4 different sides, and 6 kinds of drinks.
If he decided beforehand to get 2 different sides, how many different combinations could he order? - 120 480 360 240

Studdy Solution

STEP 1

1. Ethan can choose 1 sandwich from 5 different options.
2. Ethan can choose 2 different sides from 4 available options.
3. Ethan can choose 1 drink from 6 different options.
4. We need to find the total number of different combinations Ethan can order.

STEP 2

1. Determine the number of ways to choose the sandwich.
2. Determine the number of ways to choose 2 different sides.
3. Determine the number of ways to choose the drink.
4. Calculate the total number of combinations by multiplying the results from the previous steps.

STEP 3

Determine the number of ways to choose the sandwich.
Ethan has 5 different sandwiches to choose from.
Number of ways to choose a sandwich = 5

STEP 4

Determine the number of ways to choose 2 different sides from 4 options.
This is a combination problem where order does not matter. Use the combination formula:
$\binom{n}{r} = \frac{n!}{r!(n-r)!}$
where $n = 4$ and $r = 2$ .
$\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6$
Number of ways to choose 2 sides = 6

STEP 5

Determine the number of ways to choose the drink.
Ethan has 6 different drinks to choose from.
Number of ways to choose a drink = 6

STEP 6

Calculate the total number of combinations by multiplying the results from the previous steps.
Total combinations = (Number of ways to choose a sandwich) $\times$ (Number of ways to choose 2 sides) $\times$ (Number of ways to choose a drink)
$= 5 \times 6 \times 6 = 180$
However, the provided options do not include 180. Let's check the calculation again.

STEP 7

Re-evaluate the calculation.
Total combinations should be:
$= 5 \times 6 \times 6 = 180$
Upon re-evaluation, the calculation is correct, but the answer is not listed among the options. Let's double-check the problem statement and assumptions.

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Studdy Solution

STEP 1

1. Ethan can choose 1 sandwich from 5 different options.
2. Ethan can choose 2 different sides from 4 available options.
3. Ethan can choose 1 drink from 6 different options.
4. We need to find the total number of different combinations Ethan can order.

STEP 2

1. Determine the number of ways to choose the sandwich.
2. Determine the number of ways to choose 2 different sides.
3. Determine the number of ways to choose the drink.
4. Calculate the total number of combinations by multiplying the results from the previous steps.

STEP 3

Determine the number of ways to choose the sandwich.
Ethan has 5 different sandwiches to choose from.
Number of ways to choose a sandwich = 5

STEP 4

STEP 5

Determine the number of ways to choose the drink.
Ethan has 6 different drinks to choose from.
Number of ways to choose a drink = 6

STEP 6

STEP 7

Re-evaluate the calculation.
Total combinations should be:
$= 5 \times 6 \times 6 = 180$
Upon re-evaluation, the calculation is correct, but the answer is not listed among the options. Let's double-check the problem statement and assumptions.

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Studdy Solution

STEP 1

1. Ethan can choose 1 sandwich from 5 different options.2. Ethan can choose 2 different sides from 4 available options.3. Ethan can choose 1 drink from 6 different options.4. We need to find the total number of different combinations Ethan can order.

STEP 2

1. Determine the number of ways to choose the sandwich.2. Determine the number of ways to choose 2 different sides.3. Determine the number of ways to choose the drink.4. Calculate the total number of combinations by multiplying the results from the previous steps.

STEP 3

Determine the number of ways to choose the sandwich.Ethan has 5 different sandwiches to choose from.Number of ways to choose a sandwich = 5

STEP 4

STEP 5

Determine the number of ways to choose the drink.Ethan has 6 different drinks to choose from.Number of ways to choose a drink = 6

STEP 6

STEP 7

Re-evaluate the calculation.Total combinations should be:=5×6×6=180= 5 \times 6 \times 6 = 180=5×6×6=180Upon re-evaluation, the calculation is correct, but the answer is not listed among the options. Let's double-check the problem statement and assumptions.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Ethan can choose 1 sandwich from 5 different options.
2. Ethan can choose 2 different sides from 4 available options.
3. Ethan can choose 1 drink from 6 different options.
4. We need to find the total number of different combinations Ethan can order.

1. Determine the number of ways to choose the sandwich.
2. Determine the number of ways to choose 2 different sides.
3. Determine the number of ways to choose the drink.
4. Calculate the total number of combinations by multiplying the results from the previous steps.

Determine the number of ways to choose the sandwich.
Ethan has 5 different sandwiches to choose from.
Number of ways to choose a sandwich = 5

Determine the number of ways to choose the drink.
Ethan has 6 different drinks to choose from.
Number of ways to choose a drink = 6

Re-evaluate the calculation.
Total combinations should be:
$= 5 \times 6 \times 6 = 180$
Upon re-evaluation, the calculation is correct, but the answer is not listed among the options. Let's double-check the problem statement and assumptions.