Question

word permutations how many permutations can be made using all the letters in the word hollywood? there are permutations that can be made using all the letters.

Explanation:

Step1: Count letters and duplicates

First, we count the number of each letter in "HOLLYWOOD". The word has 9 letters: H(1), O(3), L(2), Y(1), W(1), D(1).
The formula for permutations of multiset is $\frac{n!}{n_1!n_2!...n_k!}$, where $n$ is total letters, $n_i$ are counts of each repeated letter. Here, $n = 9$, $n_O = 3$, $n_L = 2$.

Step2: Calculate factorials

Calculate $9! = 9\times8\times7\times6\times5\times4\times3\times2\times1 = 362880$, $3! = 6$, $2! = 2$.

Step3: Compute permutations

Divide: $\frac{9!}{3!2!} = \frac{362880}{6\times2} = \frac{362880}{12} = 30240$.

Answer:

30240