Question

in how many ways can the letters in the word glacier be arranged?

\\_np_r = \frac{n!}{(n-r)!}\\
\\0! = 1\\

Explanation:

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<reasoning>

Identify the number of unique letters

\[
\text{Word: GLACIER} \implies \{G, L, A, C, I, E, R\} \implies n = 7
\]

Apply the permutation formula

\[
P = 7!
\]

Calculate the final value

\[
7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
\]
</reasoning>

<answer>
5040
</answer>

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Answer:

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<reasoning>

Identify the number of unique letters

\[
\text{Word: GLACIER} \implies \{G, L, A, C, I, E, R\} \implies n = 7
\]

Apply the permutation formula

\[
P = 7!
\]

Calculate the final value

\[
7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
\]
</reasoning>

<answer>
5040
</answer>

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