# Permutations

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Permutations
Description
Exercise Name: Permutations
Math Missions: High school statistics and probability Math Mission, Precalculus Math Mission, Mathematics III Math Mission
Types of Problems: 2

The Permutations exercise appears under the High school statistics and probability Math Mission, Precalculus Math Mission and Mathematics III Math Mission. This exercise practices the concept of a permutation.

## Types of Problems

There are two types of problems in this exercise:

1. Rearrange the letters: This problem asks how many different ways the letters in a word can be rearranged. The student figure out how many ways this is possible, and answers in the available spot.
2. Put in a row: This problem asks in how many ways a subset of a given set of objects can be arranged in a row. The student figures out the answer and puts it in the available position.

## Strategies

This exercise is easy to get accuracy and speed badges because the problems are extremely consistent with the exception of the numbers.

1. The formula for picking ${r}$ items from a collection of ${n}$ is: ${\frac{n!}{(n-r)!}}$.
2. When rearranging all the letters from a word (with no repeated letters as these seem to be) the answer is the factorial of the number of letters in the word.
3. The multiplication principle can be used to solve the problems in this particular exercise.
4. Some common factorials: ${5!=120, 4!=24, 3!=6, 2!=1, 1!=1, 0!=1}$.

## Real-life Applications

1. Permutations can be applied to a lot of scenarios in real life:
1. Phone numbers.
2. Lottery (all numbers should be in a row for example: 4 8 15 16 23 42 are different from 4 8 15 16 42 23).
3. Car plates numbers (‘н 199 го’ and ‘н 919 го’** are different car plates).
4. Series numbers on products such as laptops.
5. Locker combinations.
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.