Question
Benedic wants to order a sandwich with two of the following ingredients: mushroom, eggplant, tomato, and avocado. How many different sandwiches can Benedic choose?
(1 Point)
4
6
8
(1 Point)
4
6
8
Answers
GPT-4o mini
To determine how many different sandwiches Benedic can choose with two ingredients from the list of four (mushroom, eggplant, tomato, and avocado), we can use the combination formula, which is given by:
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
Where \( n \) is the total number of ingredients (in this case, 4), and \( r \) is the number of ingredients to choose (in this case, 2).
Plugging in the values:
\[
\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4!}{2! \cdot 2!} = \frac{4 \times 3}{2 \times 1} = 6
\]
Therefore, the number of different sandwiches that Benedic can choose is \( 6 \).
So the correct answer is **6**.
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
Where \( n \) is the total number of ingredients (in this case, 4), and \( r \) is the number of ingredients to choose (in this case, 2).
Plugging in the values:
\[
\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4!}{2! \cdot 2!} = \frac{4 \times 3}{2 \times 1} = 6
\]
Therefore, the number of different sandwiches that Benedic can choose is \( 6 \).
So the correct answer is **6**.