Compute \[\binom40+\binom51+\binom62+\binom73.\
How many ways can you write two different letters, so that they are in alphabetical order? For example, AB and CT count, but ZA does not.\
Four teachers and four students are to sit around a circular table, so that each student sits directly between two teachers. How many different ways can they be seated? (Two seatings are considered the same if one can be rotated to form the other.)
