Question

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

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

Explanation:

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

$$ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 $$

Answer:

5040