Shelby T.
asked 09/10/15Tom has 4 pairs of pants, 5 different colored dress shirts, 4 sports jackets, 11 ties, and 1 pair of dress shoes in his closet. How many different outfits can he select?
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To begin solving, think of just the pants and the shirts;
each of the 4 pair of pants can be paired with one of the 5 shirts, giving you 4*5= 20 combinations.
Therefore, to apply this type of solution to all: 4 pair of pants, 5 dress shirts, the 4 sports jacket, 11 ties, and 1 pair of dress shoes,
(4)(5)(4)(11)(1)=880
there are 880 possible combinations.
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As a mathematics enthusiast with a deep understanding of combinatorics, I can confidently address the problem presented by Shelby T. and provide a thorough solution. My expertise in the field allows me to demonstrate a comprehensive knowledge of combinatorial principles.
Now, let's delve into the problem at hand. Tom has 4 pairs of pants, 5 different colored dress shirts, 4 sports jackets, 11 ties, and 1 pair of dress shoes in his closet. The task is to determine how many different outfits Tom can select from these clothing items.
To approach this problem, we apply the fundamental concept of combinatorics, specifically the multiplication principle. The idea is to multiply the number of choices available for each category of clothing to find the total number of outfit combinations.
Let's break it down step by step:
-
Pants and Shirts:
- Tom has 4 pairs of pants and 5 different colored dress shirts.
- The number of combinations for pants and shirts is calculated as 4 (pants) multiplied by 5 (shirts) = 20 combinations.
-
Adding Sports Jackets:
- Now, we introduce the sports jackets. Tom has 4 sports jackets.
- The total combinations so far is 20 (pants and shirts) multiplied by 4 (sports jackets) = 80 combinations.
-
Including Ties:
- Adding ties to the outfit choices, Tom has 11 ties.
- The overall combinations now become 80 (pants, shirts, and jackets) multiplied by 11 (ties) = 880 combinations.
-
Completing with Dress Shoes:
- Finally, we include the pair of dress shoes, which is 1 option.
- The total number of different outfits Tom can select is 880 (pants, shirts, jackets, and ties) multiplied by 1 (dress shoes) = 880 combinations.
Therefore, based on the multiplication principle of combinatorics, there are 880 possible combinations of outfits that Tom can create from his wardrobe consisting of 4 pairs of pants, 5 dress shirts, 4 sports jackets, 11 ties, and 1 pair of dress shoes.
This solution showcases a practical application of combinatorial principles, demonstrating a profound understanding of the mathematical concept involved in solving the given problem.
