Question

how many permutations of Niotca are there?

Answer 1

You mean how many 6-letter "words" can you create witht he letters of "Niotca"?

Answer 2

I think that's what he means.
For the first letter of your new six-letter word, there are 6 possibilities. There are five for the second letter because you already used a letter, then 4, then 3, then 2, then 1.
So the number of permutations is 6*5*4*3*2*1, or 6! if you've learned factorial notation.
Hope that helps. :)