You have n numbers that must sum to 10. So your first number plus your second
number, plus all the way to the nth number, has to equal 10. You may choose a
certain number of values, these xi's, any way you wish. But then a certain
number of values are forced, so that they sum to 10. How many degrees of
freedom are there? Or in other words, how many values may you choose any way
you wish. This is tricky.