# A Software Engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. How many days can the software engineer go without wearing the same combination of three items?

Explore the fashion possibilities of a software engineer's closet: 3 pants, 4 shirts, and 3 pairs of shoes. Learn the number of distinct outfit combinations they can mix and match!

by Maivizhi A

**Updated **Mar 06, 2024

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## A Software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. How many days can the software engineer go without wearing the same combination of three items?

The software engineer can go without wearing the same combination of three items for 36 days.

To calculate the number of unique combinations of three items (pants, shirt, and shoes) that the software engineer can wear without repeating the same combination, you multiply the number of options for each item.

Number of pants = 3

Number of shirts = 4

Number of shoes = 3

So, the total number of unique combinations of three items is:

3 (pants) * 4 (shirts) * 3 (shoes) = 36

Therefore, the software engineer can go without wearing the same combination of three items for 36 days.

## What are Combinations and Permutations?

Combinations and permutations are concepts in combinatorial mathematics that deal with the arrangement and selection of objects from a set.

Permutations: A permutation refers to the arrangement of objects in a specific order. In other words, it is the number of different ways in which a set of objects can be arranged. The order matters in permutations. For example, if you have a set of objects {A, B, C}, the permutations could be ABC, ACB, BAC, BCA, CAB, or CBA. The number of permutations of n distinct objects taken r at a time is denoted by P(n, r) and is calculated using the formula:

P(n, r) = n! / (n - r)!

where n! denotes the factorial of n, which is the product of all positive integers up to n.

Combinations: A combination, on the other hand, refers to the selection of objects from a set without considering the order. In combinations, the order doesn't matter. For example, using the set {A, B, C}, the combinations could be AB, AC, or BC. The number of combinations of n distinct objects taken r at a time is denoted by C(n, r) and is calculated using the formula:

C(n, r) = n! / (r!(n - r)!)

This formula represents the number of ways to choose r objects from a set of n objects without considering the order.

In summary, permutations deal with arrangements where order matters, while combinations deal with selections where order doesn't matter.

## A software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes. How many days can the software engineer go without wearing the same combination of three items - FAQs

### 1. What is the total number of items the software engineer owns?

The software engineer owns 3 pairs of pants, 4 shirts, and 3 pairs of shoes, totaling 10 items.

### 2. Why is it important to calculate unique combinations?

Calculating unique combinations helps ensure variety and prevents the repetition of outfits, adding freshness to the wardrobe.

### 3. Can the software engineer repeat a single item within a combination?

Yes, the software engineer can repeat a single item within a combination, as long as the overall combination is unique.

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