in how many ways can the letters in the word spoon be arranged?\no 24\no 30\no 60\no 120
in how many ways can the letters in the word spoon be arranged?\no 24\no 30\no 60\no 120
Answer
Explanation:
Step1: Identify total and repeated letters
The word "spoon" has 5 letters in total, with 2 'o's.
Step2: Use permutation formula for repeated - elements
The formula for permutations of (n) objects where (p_1) of one kind, (p_2) of another kind, (\cdots), (p_k) of the (k) - th kind are identical is (\frac{n!}{p_1!p_2!\cdots p_k!}). Here (n = 5) and (p_1=2) (for the 2 'o's), so the number of arrangements is (\frac{5!}{2!}).
Step3: Calculate factorial values
We know that (n!=n\times(n - 1)\times\cdots\times1). So (5!=5\times4\times3\times2\times1 = 120) and (2!=2\times1=2).
Step4: Compute the result
(\frac{5!}{2!}=\frac{120}{2}=60).
Answer:
60