# Combinations

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The Combinations exercise appears under the High school statistics and probability Math Mission, Precalculus Math Mission and Mathematics III Math Mission. This exercise practices calculating combinations.

## Types of Problems

There is one type of problem in this exercise:

1. Perform combination: This problem describes a situation where a collection of objects is selected from a larger group and the order does not matter. The user is supposed to find how many combinations are possible and place that answer in the appropriate area.

## Strategies

This exercise is easy to get accuracy and speed badges because there is only one type of problem and the formula is straightforward. Speed badges are especially easy if users know how to use a calculator to calculate combinations.

1. The formula for ${r}$ objects being chosen from a collection of n (order does not matter) is ${\frac{n!}{((n-r)!r!)}}$.
2. Some useful factorials to know are ${5!=120, 4!=24, 3!=6, 2!=2, 1!=1, 0!=1}$.
3. If the user has ${n}$ objects and you need to select ${r}$, users can write a fraction with ${r}$ slots in the numerator and ${r}$ slots in the denominator. Write decreasing consecutive numbers starting from ${n}$ in the numerator, and decreasing consecutive numbers starting from ${r}$ in the denominator. Simplify, and that is the answer.
4. The solution to a combination is always an integer. If users are not getting an integer, they calculated incorrectly.

## Real-life Applications

1. Combinations are used oftenly, for example:
1. Teacher taking attendance
2. Selecting nominees for user council
3. Card games such as poker
4. Voting (no matter who votes first)
5. Making a sandwich (no matter in what order the toppings are)
2. Data and statistics appear in news reports and in the media every day.
3. Statistics can be seen more frequently than calculus in every day life.