Bill Boston's Omaha High-Low 5,277 hands

[chaos]

On the cover and throughout the text of the 4th edition of Bill Boston's Omaha High-Low book, he refers to there being 5,277 possible hands and his master table contains that many hands. In a few places he mentions 5,232 possible hands. I decided to do a count for myself.

Using his method of tabulation, I divided the possible hands into the following categories:
AAAA NS
AAAB S NS
AABB DS S NS
AABC DS S NS
ABCD DS S NS

I'll work through AABC. There are 13 ways to choose the value of the pair, 12 ways to choose the value of the first non-pairing card and 11 ways to choose the value of the second non-pairing card. We need to divide by two since we do not want to count AABC and AACB twice. Since there are three varieties of AABC hands (namely DS, S, and NS) we multiply by 3. Performing similar calculations for the other hand types yields:
AAAA 13 * 1 = 13
AAAB 13 * 12 * 2 = 312
AABB 13 * 12 * 3 / 2 = 234
AABC 13 * 12 * 11 * 3 / 2 = 2574
ABCD 13 * 12 * 11 * 10 * 3 / 24 = 2145

Summing yields 5,278 hands or one more than Bill Boston has in his table.