# How many different ways are there to arrange the 6 letters in the word SUNDAY?

Dec 19, 2016

There are 720 different ways to arrange the 6 letters in SUNDAY.

#### Explanation:

The first letter of the rearrangement can be any 1 of 6 letters.

The second letter can now be any 1 of 5 letters. So the first two letters can be a combination of $\textcolor{red}{6 \times 5}$ letters or $\textcolor{red}{30}$ arrangements.

The third letter can be any 1 of 4 remaining letters. So the first three letters can be a combination of $\textcolor{red}{6 \times 5 \times 4}$ letters or $\textcolor{red}{120}$ arrangements.

The fourth letter can now be any 1 of 3 remaining letters. So the first four letters can be a combination of $\textcolor{red}{6 \times 5 \times 4 \times 3}$ letters or $\textcolor{red}{360}$ arrangements.

The fifth letter can now be only 1 of 2 remaining letters. So the first five letters can be a combination of $\textcolor{red}{6 \times 5 \times 4 \times 3 \times 2}$ letters or $\textcolor{red}{720}$ arrangements.

The final letter can now be only 1 letter because all of the others have been used. So the six letters can be a combination of $\textcolor{red}{6 \times 5 \times 4 \times 3 \times 2 \times 1}$ letters or $\textcolor{red}{720}$ arrangements.