An auctioneer is preparing to auction off some items in an estate sale. In how many different orders can a famous painting, an heirloom necklace, and a vintage record collection be presented at the auction?
Question
An auctioneer is preparing to auction off some items in an estate sale. In how many different orders can a famous painting, an heirloom necklace, and a vintage record collection be presented at the auction?
Solution
This is a problem of permutations. In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order.
Here, we have 3 items: a famous painting, an heirloom necklace, and a vintage record collection. We want to know in how many different orders these items can be presented.
The formula for permutations is n!, where n is the number of items, and "!" denotes factorial, which means multiplying all positive integers from our chosen number down to 1.
So, for 3 items, the number of permutations is 3! = 3 * 2 * 1 = 6.
Therefore, the auctioneer can present the items in 6 different orders.
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