Question

Sofia's taco truck lets customers choose 3 ingredients from the list below to add to their tacos: onions, cheese, cilantro, crema, jalapeño, salsa. How many groups of 3 different ingredients can go on a taco?

a) 10
b) 15
c) 20
d) 60

Answer 1

The student can choose 3 different ingredients out of 6 in 20 unique ways for their taco, per the combinations formula C(n, k) in combinatorics.

Step-by-step explanation:

The question asks how many groups of 3 different ingredients can be chosen for Sofia's taco from a list of 6 ingredients. This is a problem of combinations in mathematics, specifically combinatorics. To solve this, we use the combination formula, which is C(n, k) = n! / (k!(n-k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, and '!' represents the factorial of a number.

In this case, 'n' is 6 (because there are 6 ingredients) and 'k' is 3 (because we are choosing 3 ingredients). Using the combination formula, C(6, 3) = 6! / (3!(6-3)!) = (6*5*4) / (3*2*1) = 20. Therefore, there are 20 different ways to choose 3 ingredients from the list.