Patient Age Avg Visits / Year
<1 year 7.5
1-4 years 3.0
5-14 years 1.8
15-24 years 1.7
25-44 years 2.6
45-64 years 4.0
65-74 years 6.7
>75 years 8.2

The table above breaks out, by age range, the average number of visits people make to physicians each year. If you were an insurance company that wanted a member mix that would average 50 physician visits per year, you could sign up either of the following two member mixes:

10 members in the "1-4 years" age range and
5 members in the "45-64 years" age range
resulting in (10 x 3.0) + (5 x 4.0) = 50

2 members in the "<1 year" age range,
10 members in the "5-14 years" age range and
10 members in the "15-24 years" age range
resulting in (2 x 7.5) + (10 x 1.8) + (10 x 1.7) = 50

Note that there are many more possibilities.

Question 1: What is the total number of different member mixes that result in 50 physician visits per year?
Question 2: What is the total number of different member mixes that result in 200 physician visits per year?
Question 3: What is the total number of different member mixes that result in 5000 physician visits per year?