Question

select the correct answer. consider the word grateful. if all of the letters are used, how many ways can the letters be arranged? a. 36 b. 720 c. 5,040 d. 40,320

Explanation:

Step1: Count unique letters

The word "grateful" has 8 distinct letters: g, r, a, t, e, f, u, l.

Step2: Calculate permutations

For \(n\) distinct items, the number of full permutations is \(n!\). Here \(n=8\), so compute \(8!\):
$$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$$

Answer:

D. 40,320