Anagrams of PANNELLO

Text

How many anagrams (words, meaningful or not) can be formed from the letters of the word PANNELLO?

Solution

The word has $8$ letters but with repetitions: N appears $2$ times and L appears $2$ times (the others — P, A, E, O — once each). These are permutations with repetition: $N = \frac{8!}{2!\,\cdot\,2!} = \frac{40\,320}{4} = \boxed{10\,080}.$