Question

A company has received 20 purchase orders. The shipping department has been given 8 orders to fill. There are _____ different orders the shipping department could be given to fill. (answer should be numbers only - no commas).

Answer 1

The number of different orders the shipping department could be given to fill from 20 orders when given 8 to process is calculated using combinations, specifically C(20, 8).

Step-by-step explanation:

The question asks for the number of different orders the shipping department could be given to fill from a total of 20 purchase orders when they are given 8 to process. This can be solved using the combination formula for selecting 8 orders out of 20 without regard for order, which is denoted as C(n, k) or nCk, where n is the total number of items to choose from, k is the number of items to choose, and the formula is C(n, k) = n! / (k!(n-k)!). Applying this, we have C(20, 8) = 20! / (8!12!). The solution to this gives us the number of different combinations possible.