# MAT - Paper 2018 - Q5

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q5/ · Updated: 2021-10-28 · Tags: mat, notes, maths

## Flashcards
### 2021-10-28
##### How is working out a formula for the number of possibilities similar to working out probabilities??
You add separate cases and multiply possibilities within a case.

##### ![PHOTO TOWER POSSIBLE](tower-possible.png) Let $t_n$ denote the number of possibilities for an $n$-tower. So $t_1$ means the number of possibilities for a $1$-tower and $t_2$ means the number of possibilities for a $2$-tower. Since this is recursive, how could you write a formula in terms of $t_{n-1}$, $t_{n-2}$ etc. for the number of possibilities for $t_n$??
![PHOTO TOWER FORMULA](tower-formula.png)

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