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Neha is playing a word game where she's trying to make 3 -letter words using letters in the word TIGER. She cannot use the same letter twice.
How many unique ways are there to arrange 3 letters from the word TIGER?

Neha is playing a word game where she's trying to make $3$ -letter words using letters in the word TIGER. She cannot use the same letter twice. $\newline$ How many unique ways are there to arrange $3$ letters from the word TIGER?

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Counting principle

Full solution

Q. Neha is playing a word game where she's trying to make

3

-letter words using letters in the word TIGER. She cannot use the same letter twice.

\newline

How many unique ways are there to arrange

3

letters from the word TIGER?

Determine first letter choices: Determine the number of choices for the first letter. $\newline$ Neha can choose any of the $5$ letters from the word TIGER for the first letter of her $3$ -letter word. $\newline$ Choices for the first letter $= 5$
Determine second letter choices: Determine the number of choices for the second letter. $\newline$ After choosing the first letter, Neha has $4$ remaining letters to choose from for the second letter, since she cannot repeat the letter she already used. $\newline$ Choices for the second letter $= 4$
Determine third letter choices: Determine the number of choices for the third letter. $\newline$ After choosing the first and second letters, Neha has $3$ remaining letters to choose from for the third letter. $\newline$ Choices for the third letter $= 3$
Calculate total unique words: Calculate the total number of unique $3$ -letter words. $\newline$ Using the basic counting principle, we multiply the number of choices for each position together to find the total number of unique words. $\newline$ Total unique $3$ -letter words = Choices for the first letter $\times$ Choices for the second letter $\times$ Choices for the third letter $\newline$ Total unique $3$ -letter words = $5 \times 4 \times 3$ $\newline$ Total unique $3$ -letter words = $60$

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