Number of Arrangements of n Objects of m Types/Examples/Letters in added

Example of Use of Number of Arrangements of $n$ Objects of $m$ Types
Let $N$ be the number of different arrangements of the letters in the word $\texttt{added}$.

Then:
 * $N = 20$

Proof
There are $3$ types of letter in $\texttt{added}$, that is:


 * $\texttt a$: $1$ instance
 * $\texttt d$: $3$ instances
 * $\texttt e$: $1$ instance

Hence we have an instance of Number of Arrangements of $n$ Objects of $m$ Types, such that:
 * $n = 5$
 * $k_1 = 1$
 * $k_2 = 3$
 * $k_3 = 1$

Hence we have:
 * $N = \dfrac {5!} {1! \times 3! \times 1!} = \dfrac {120} 6 = 20$

Hence the result.