Question

in how many ways can the letters in the word spoon be arranged?
24
30
60
120

Explanation:

Step1: Identify the letters and duplicates

The word "spoon" has 5 letters, with the letter 'o' repeated 2 times.

Step2: Use the permutation formula for repeated elements

The formula for permutations of a word with \( n \) total letters and \( n_1, n_2, \dots, n_k \) repeated letters is \( \frac{n!}{n_1! \cdot n_2! \cdot \dots \cdot n_k!} \). Here, \( n = 5 \) and \( n_1 = 2 \) (for 'o'). So we calculate \( \frac{5!}{2!} \).

Step3: Calculate the factorials

\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \), \( 2! = 2 \times 1 = 2 \).

Step4: Divide to get the result

\( \frac{120}{2} = 60 \).

Answer:

60