How many ways are there to arrange 4 letters from “combinatorics”?
So I’m studying about combinatorics and permutations. And I stuck with this question. So I just doing my own step but I want to make sure that it’s correct or not.
thank you very much and sorry about my bad grammar :)
Your work is mostly fine.
However, for case $1$ (no letters the same), it should be $^{10}P_4 = \ ^{10}C_4 \cdot 4! = \ ^{10}C_\color{red}{6} \cdot 4!$. It would be better to write this number as a permutation, as which order you place the numbers matters.