A restaurant is adding ranch dressing, blue cheese dip, and broccoli to its salad bar. In how many different orders could the manager decide to arrange the items in a row along the salad bar?
Question
A restaurant is adding ranch dressing, blue cheese dip, and broccoli to its salad bar. In how many different orders could the manager decide to arrange the items in a row along the salad bar?
Solution
This is a permutation problem. Permutations are the various ways in which objects from a set may be selected, generally without replacement, and arranged in a sequence.
In this case, we have 3 items: ranch dressing, blue cheese dip, and broccoli.
The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items, and r is the number of items to choose.
However, since we are arranging all the items (ranch dressing, blue cheese dip, and broccoli), r is equal to n. So, the formula simplifies to n!, which is the factorial of n.
The factorial of a number is the product of all positive integers less than or equal to that number.
So, for this problem, we need to find 3!, which is 321 = 6.
Therefore, the manager could arrange the items in 6 different orders along the salad bar.
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