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Mateo is playing a word game where he's trying to make 4 -letter words by rearranging the letters in the word IRON.
How many unique ways are there to arrange the letters in the word IRON?

Mateo is playing a word game where he's trying to make $4$ -letter words by rearranging the letters in the word IRON. $\newline$ How many unique ways are there to arrange the letters in the word IRON?

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Counting principle

Full solution

Q. Mateo is playing a word game where he's trying to make

4

-letter words by rearranging the letters in the word IRON.

\newline

How many unique ways are there to arrange the letters in the word IRON?

Count of Letters: There are $4$ letters in the word IRON, so the first position can be filled by any of the $4$ letters.
Choosing First Letter: After choosing the first letter, there are $3$ letters left for the second position.
Choosing Second Letter: Then, there are $2$ letters left for the third position.
Choosing Third Letter: Finally, there's only $1$ letter left for the last position.
Choosing Last Letter: So, the total number of unique ways to arrange the letters is $4 \times 3 \times 2 \times 1$ .
Total Number of Arrangements: Calculating that gives us $4 \times 3 \times 2 \times 1 = 24$ .

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