91影视

The letters of the word 鈥渉omoscedasticity鈥� are to be arranged.

The number of unique ways to arrange n items where few of them are of same type is established using following formula.

The following is its formula:

$\frac{n!}{n_1!脳n_2!脳....脳n_k!}$

Here, out of a total of n items, $n_1$ are alike, $n_2$ are alike, and it continues until $n_k$ are alike.

The total number of letters is 16.

The letters that are identical or repetitive are 鈥渙,鈥� 鈥渟,鈥� 鈥渃,鈥� 鈥渢,鈥� and 鈥渋鈥�.

Here,the letters 鈥渙,鈥� 鈥渟,鈥� 鈥渃,鈥� 鈥渢,鈥� and 鈥渋鈥� are all repeating twice.

The number of ways in which the 16 letters can be arranged is determined below:

$$\begin{gathered} \frac{n!}{n_1!脳n_2!脳....脳n_k!}=\frac{16!}{2!鈥�脳2!脳2!脳2!脳2!} \\ =653,837,184,000 \end{gathered}$$

Therefore, the number of unique ways in which the letters of the word 鈥渉omoscedasticity鈥� can be arranged is 653,837,184,000.