Suppose . How many -tuples are there for which each and ?
introduce anouter variable a≥1, and let Clearly, Now, we solve this equality. Subtract one from both sides, and let u=a-1. Then u≥0--like the other variables. So now, we have n-1 on the RHS and k+1=>k + signs. So, there are (n-1+k, n-1) solutions to the inequality.