in how many ways can the letters in the word spoon be arranged?\n24\n30\n60\n120

Explanation:

Step1: Determine total - letter count

The word "spoon" has 5 letters.

Step2: Account for repeated letters

The letter 'o' is repeated 2 times. The formula for permutations of a word with repeated letters is $\frac{n!}{r!}$, where $n$ is the total number of letters and $r$ is the number of times a letter is repeated. Here, $n = 5$ and $r = 2$. The factorial of a non - negative integer $n$, denoted by $n!$, is $n\times(n - 1)\times\cdots\times1$. So, $5! = 5\times4\times3\times2\times1=120$ and $2! = 2\times1 = 2$.

Step3: Calculate the number of arrangements

The number of arrangements is $\frac{5!}{2!}=\frac{120}{2}=60$.

Answer:

60