A jewelry store sells a necklace that the buyer can customize. The buyer is instructed to select 2 different charms from among the 8 available and specify the order from left to right. How many different necklaces are possible?
Question
A jewelry store sells a necklace that the buyer can customize. The buyer is instructed to select 2 different charms from among the 8 available and specify the order from left to right. How many different necklaces are possible?
Solution
To solve this problem, we can use the concept of permutations in combinatorics.
Step 1: Understand the problem The buyer needs to select 2 different charms out of 8 and the order in which they are arranged matters. This is a permutation problem.
Step 2: Apply the formula for permutations The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Step 3: Substitute the given values into the formula In this case, n = 8 (the total number of charms) and r = 2 (the number of charms to choose). So, the calculation becomes 8P2 = 8! / (8 - 2)!
Step 4: Simplify the calculation 8! / (8 - 2)! = 8! / 6! = 8*7 = 56
So, there are 56 different necklaces possible.
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