Homework problems

Problem11. Each box in a $2\times2$ table can be colored black or white. How many different colorings of the table are there.
Problem12. How many ways are there to put one white and one black king on a chessboard so that they do not attack each other?
Problem13. How many ``words'' can be obtained by rearranging the word ``MATHEMATICAL''?
Problem14. There are six letters in the Hermetian language. A word is any sequence of six letters, some pair of which are the same. How many words are there in the Hermetian language?
Answer. 6⁶-6!