Question

Your school cafeteria has purchased enough food for 12 different lunches over the next few weeks. Due to a holiday on Monday, there are only 4 school days this week. How many different ways are there for the cafeteria to select and arrange 4 of these lunches to serve?

Answer 1

There are 11,880 different ways for the cafeteria to select and arrange 4 out of the 12 lunches, calculated using the permutations formula.

Step-by-step explanation:

The school cafeteria is looking for the number of different ways to select and arrange 4 lunches out of 12 options. This problem involves permutations since the order of the lunches matters. We use the formula for permutations without repetition, which is nPr = n! / (n - r)!, where n is the total number of items to choose from, and r is the number of items we want to arrange.

In this case, n is 12 and r is 4, so the calculation would be:

12P4 = 12! / (12 - 4)! = 12! / 8! = (12 × 11 × 10 × 9) × (8! / 8!) = 12 × 11 × 10 × 9 = 11,880.

Therefore, there are 11,880 different ways for the cafeteria to select and arrange 4 out of the 12 lunches.