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