Question

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

Explanation:

Step1: Identify the letters and duplicates

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

Step2: Use permutation formula for repeated elements

The formula for permutations of a word with \( n \) total letters and \( r \) repeated letters is \( \frac{n!}{r!} \). Here, \( n = 5 \) and \( r = 2 \).

Step3: Calculate factorials

\( 5! = 5\times4\times3\times2\times1 = 120 \), \( 2! = 2\times1 = 2 \).

Step4: Divide to find the number of arrangements

\( \frac{5!}{2!} = \frac{120}{2} = 60 \).

Answer:

60