Question

You work as a health inspector and must visit each of the 17 restaurants in town once each week. What is the number of different orders for every Friday if you have to visit 5 restaurants every Friday.

Answer 1

The number of different orders to visit 5 restaurants out of 17 each Friday is computed using the combination formula, resulting in 6188 possible combinations.

Step-by-step explanation:

The student is asking about the number of different ways to visit 5 restaurants out of 17 available each Friday. This is a combinatorics question that deals with combinations. To find the number of different orders in which you can visit 5 out of 17 restaurants, you use the combination formula:

C(n, k) = n! / (k!(n-k)!), where 'n' represents the total number of items, 'k' represents the number of items to choose, '!' denotes factorial, and 'C' represents the combination. Applying this formula:

C(17, 5) = 17! / (5!*(17-5)!) = 6188 possible combinations.