First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.
The inverse operation of division is multiplication <span />
Factor the denominators.
Adjust fractions based on LCM.
Denominators are same, so add the fractions.
Expand the numerator.
