1. Find the generating function for the ways of distributing n loonies to 5 people so that the first two people have together either at most 8 loonies or an even number.
2. How many 9 digit numbers are there whose sum of digits is equal to 24?
For #1, I know how to find the generating function if the first two people have at most 8 loonies together AND an even number. But I am not sure how to approach this problem.
For #2, isn't this equivalent to asking how many solutions there are to to x1+x2+...+x9=24 with x1=>1? My solution is as follows: C(23+9-1, 9-1) - C(23+8-1, 8-1) = C(31,8) - C(30-7) = 5,852,925. But apparently the answer is 5,949,615.
Any help would be appreciated.