Question

A bbq restaurant lets the customer choose 3 sides to accompany their entree. If the restaurant offers 5 different sides, how many different combinations of sides can a customer choose?

1) 10
2) 15
3) 20
4) 25

Answer 1

Using the formula for combinations C(n, r) = n! / [r!(n-r)!], we find that there are 10 different combinations of 3 sides that a customer can choose from 5 available options at the BBQ restaurant.

Step-by-step explanation:

The question deals with finding the number of different combinations of sides a customer can choose if there are 5 different sides available and the customer can choose 3. To calculate this, we use combinations, which are selections where the order does not matter. The mathematical formula for combinations is:
C(n, r) = n! / [r!(n-r)!]
Where C(n, r) is the number of combinations, n is the total number of items to choose from, and r is the number of items to pick. Plugging in the numbers from the question:
C(5, 3) = 5! / [3!(5-3)!] = (5 × 4 × 3 × 2 × 1) / [(3 × 2 × 1)(2 × 1)]

After simplifying:
C(5, 3) = 10

This means there are 10 different combinations of sides that a customer can choose from the BBQ restaurant's menu.