MAT - Paper 2018 - Q5
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.
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 $t _ n$?
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 $t _ n$?