This problem can be solved using the concept of permutations in combinatorics.

Step 1: Understand the problem. Sidney has 5 shirts and she wants to choose 3 of them to wear on a trip. The order in which she wears the shirts matters (i.e., wearing shirt A, then B, then C is different from wearing shirt B, then A, then C).

Step 2: Use 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 (the product of all positive integers up to that number).

Step 3: Plug in the numbers. In this case, n = 5 (the total number of shirts) and r = 3 (the number of shirts to choose). So the calculation would be 5P3 = 5! / (5 - 3)!.

Step 4: Calculate the factorials. 5! = 5 * 4 * 3 * 2 * 1 = 120, and (5 - 3)! = 2! = 2 * 1 = 2.

Step 5: Divide to find the answer. 120 / 2 = 60.

So, there are 60 different sequences in which Sidney can wear the 3 shirts over the 3 days.

Question

This problem can be solved using the concept of permutations in combinatorics.

Step 1: Understand the problem. Sidney has 5 shirts and she wants to choose 3 of them to wear on a trip. The order in which she wears the shirts matters (i.e., wearing shirt A, then B, then C is different from wearing shirt B, then A, then C).

Step 2: Use 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 (the product of all positive integers up to that number).

Step 3: Plug in the numbers. In this case, n = 5 (the total number of shirts) and r = 3 (the number of shirts to choose). So the calculation would be 5P3 = 5! / (5 - 3)!.

Step 4: Calculate the factorials. 5! = 5 * 4 * 3 * 2 * 1 = 120, and (5 - 3)! = 2! = 2 * 1 = 2.

Step 5: Divide to find the answer. 120 / 2 = 60.

So, there are 60 different sequences in which Sidney can wear the 3 shirts over the 3 days.

Knowee AI · Accepted Answer

This problem can be solved using the concept of permutations in combinatorics.

Step 1: Understand the problem. Sidney has 5 shirts and she wants to choose 3 of them to wear on a trip. The order in which she wears the shirts matters (i.e., wearing shirt A, then B, then C is different from wearing shirt B, then A, then C).

Step 2: Use 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 (the product of all positive integers up to that number).

Step 3: Plug in the numbers. In this case, n = 5 (the total number of shirts) and r = 3 (the number of shirts to choose). So the calculation would be 5P3 = 5! / (5 - 3)!.

Step 4: Calculate the factorials. 5! = 5 * 4 * 3 * 2 * 1 = 120, and (5 - 3)! = 2! = 2 * 1 = 2.

Step 5: Divide to find the answer. 120 / 2 = 60.

So, there are 60 different sequences in which Sidney can wear the 3 shirts over the 3 days.

Sidney bought 5 new shirts at the store today, and she plans to pack 3 of them to wear on a trip that will last 3 days. How many sequences of 3 shirts are possible?

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