# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-numbers-permutation-combinations.html


## Permutations and Combinations

""Mathematically, boy," he told himself, "if nobody else original comes along, they're bound to run out of arrangements someday. What then?" What indeed. This sort of arranging and rearranging was Decadence, but the exhaustion of all possible permutations and combinations was death. It scared Eigenvalue, sometimes. He would go in back and look at the set of dentures. Teeth and metals endure" Thomas Pynchon


#### Permutations


##### Prior Knowledge

- Binomial coefficient
- You must be able to manipulate algebraic expressions. (If not, check this lesson)
- You must be able to manipulate exponential expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Read this presentation
- 3. Watch this solved problem

#### Combinations


##### Prior Knowledge

- To be able find terms and the sum of a geometric sequence.

##### Key Points

- 1. Watch the video:

#### Extra


##### Material and references:

- Hodder Book HL(ISBN: 9781510462366) : 1A, 1B

##### Key Points

- You should be able to find the number of ways of choosing an option from list \( A \) and an option from list \( B \). The AND rule is \[ n(A \text{ AND } B) = n(A)\times n(B). \]
- 2. You should be able to find the number of ways of choosing an option from list \( A \) or an option from list \( B \). The OR rule (when \( A \) and \( B \) are mutually exclusive) is \[ n(A \text{ OR } B) = n(A) + n(B). \]
- 3. You should be able to find the number of permutations of \( n \) items. The number of permutations of \( n \) items is \[ n!. \]
- You should be able to find the number of ways of choosing \( r \) items from a list of \( n \) items. The number of combinations of \( r \) objects out of \( n \) (when order does not matter) is \[ {^nC_r} = \frac{n!}{r!(n-r)!}. \] The number of permutations of \( r \) objects out of \( n \) (when order does matter) is \[ {^nP_r} = \frac{n!}{(n-r)!}. \]

### IB Past Paper Problems

Select a topic and unit, then click the button below to get a new problem.

Press the button to start!

How was this problem?