D&D 5E How Many Point Buy Options

[Oofta]

If you want to allow up to an 18 (using 3.5 options for point buy) and 28 points you get
18, 14, 9, 8, 8, 8
18, 13, 11, 8, 8, 8
18, 13, 10, 9, 8, 8
18, 13, 9, 9, 9, 8
18, 12, 12, 8, 8, 8
18, 12, 11, 9, 8, 8
18, 12, 10, 10, 8, 8
18, 12, 10, 9, 9, 8
18, 12, 9, 9, 9, 9
18, 11, 11, 10, 8, 8
18, 11, 11, 9, 9, 8
18, 11, 10, 10, 9, 8
18, 11, 10, 9, 9, 9
18, 10, 10, 10, 10, 8
18, 10, 10, 10, 9, 9
17, 16, 8, 8, 8, 8
17, 15, 11, 8, 8, 8
17, 15, 10, 9, 8, 8
17, 15, 9, 9, 9, 8
17, 14, 13, 8, 8, 8
17, 14, 12, 9, 8, 8
17, 14, 11, 10, 8, 8
17, 14, 11, 9, 9, 8
17, 14, 10, 10, 9, 8
17, 14, 10, 9, 9, 9
17, 13, 13, 10, 8, 8
17, 13, 13, 9, 9, 8
17, 13, 12, 11, 8, 8
17, 13, 12, 10, 9, 8
17, 13, 12, 9, 9, 9
17, 13, 11, 11, 9, 8
17, 13, 11, 10, 10, 8
17, 13, 11, 10, 9, 9
17, 13, 10, 10, 10, 9
17, 12, 12, 12, 8, 8
17, 12, 12, 11, 9, 8
17, 12, 12, 10, 10, 8
17, 12, 12, 10, 9, 9
17, 12, 11, 11, 10, 8
17, 12, 11, 11, 9, 9
17, 12, 11, 10, 10, 9
17, 12, 10, 10, 10, 10
17, 11, 11, 11, 11, 8
17, 11, 11, 11, 10, 9
17, 11, 11, 10, 10, 10
16, 16, 12, 8, 8, 8
16, 16, 11, 9, 8, 8
16, 16, 10, 10, 8, 8
16, 16, 10, 9, 9, 8
16, 16, 9, 9, 9, 9
16, 15, 14, 8, 8, 8
16, 15, 13, 10, 8, 8
16, 15, 13, 9, 9, 8
16, 15, 12, 11, 8, 8
16, 15, 12, 10, 9, 8
16, 15, 12, 9, 9, 9
16, 15, 11, 11, 9, 8
16, 15, 11, 10, 10, 8
16, 15, 11, 10, 9, 9
16, 15, 10, 10, 10, 9
16, 14, 14, 10, 8, 8
16, 14, 14, 9, 9, 8
16, 14, 13, 12, 8, 8
16, 14, 13, 11, 9, 8
16, 14, 13, 10, 10, 8
16, 14, 13, 10, 9, 9
16, 14, 12, 12, 9, 8
16, 14, 12, 11, 10, 8
16, 14, 12, 11, 9, 9
16, 14, 12, 10, 10, 9
16, 14, 11, 11, 11, 8
16, 14, 11, 11, 10, 9
16, 14, 11, 10, 10, 10
16, 13, 13, 13, 9, 8
16, 13, 13, 12, 10, 8
16, 13, 13, 12, 9, 9
16, 13, 13, 11, 11, 8
16, 13, 13, 11, 10, 9
16, 13, 13, 10, 10, 10
16, 13, 12, 12, 11, 8
16, 13, 12, 12, 10, 9
16, 13, 12, 11, 11, 9
16, 13, 12, 11, 10, 10
16, 13, 11, 11, 11, 10
16, 12, 12, 12, 12, 8
16, 12, 12, 12, 11, 9
16, 12, 12, 12, 10, 10
16, 12, 12, 11, 11, 10
16, 12, 11, 11, 11, 11
15, 15, 15, 9, 8, 8
15, 15, 14, 11, 8, 8
15, 15, 14, 10, 9, 8
15, 15, 14, 9, 9, 9
15, 15, 13, 13, 8, 8
15, 15, 13, 12, 9, 8
15, 15, 13, 11, 10, 8
15, 15, 13, 11, 9, 9
15, 15, 13, 10, 10, 9
15, 15, 12, 12, 10, 8
15, 15, 12, 12, 9, 9
15, 15, 12, 11, 11, 8
15, 15, 12, 11, 10, 9
15, 15, 12, 10, 10, 10
15, 15, 11, 11, 11, 9
15, 15, 11, 11, 10, 10
15, 14, 14, 13, 8, 8
15, 14, 14, 12, 9, 8
15, 14, 14, 11, 10, 8
15, 14, 14, 11, 9, 9
15, 14, 14, 10, 10, 9
15, 14, 13, 13, 10, 8
15, 14, 13, 13, 9, 9
15, 14, 13, 12, 11, 8
15, 14, 13, 12, 10, 9
15, 14, 13, 11, 11, 9
15, 14, 13, 11, 10, 10
15, 14, 12, 12, 12, 8
15, 14, 12, 12, 11, 9
15, 14, 12, 12, 10, 10
15, 14, 12, 11, 11, 10
15, 14, 11, 11, 11, 11
15, 13, 13, 13, 12, 8
15, 13, 13, 13, 11, 9
15, 13, 13, 13, 10, 10
15, 13, 13, 12, 12, 9
15, 13, 13, 12, 11, 10
15, 13, 13, 11, 11, 11
15, 13, 12, 12, 12, 10
15, 13, 12, 12, 11, 11
15, 12, 12, 12, 12, 11
14, 14, 14, 14, 8, 8
14, 14, 14, 13, 10, 8
14, 14, 14, 13, 9, 9
14, 14, 14, 12, 11, 8
14, 14, 14, 12, 10, 9
14, 14, 14, 11, 11, 9
14, 14, 14, 11, 10, 10
14, 14, 13, 13, 12, 8
14, 14, 13, 13, 11, 9
14, 14, 13, 13, 10, 10
14, 14, 13, 12, 12, 9
14, 14, 13, 12, 11, 10
14, 14, 13, 11, 11, 11
14, 14, 12, 12, 12, 10
14, 14, 12, 12, 11, 11
14, 13, 13, 13, 13, 9
14, 13, 13, 13, 12, 10
14, 13, 13, 13, 11, 11
14, 13, 13, 12, 12, 11
14, 13, 12, 12, 12, 12
13, 13, 13, 13, 13, 11
13, 13, 13, 13, 12, 12

And for "heroic" tier (32 points)
18, 16, 8, 8, 8, 8
18, 15, 11, 8, 8, 8
18, 15, 10, 9, 8, 8
18, 15, 9, 9, 9, 8
18, 14, 13, 8, 8, 8
18, 14, 12, 9, 8, 8
18, 14, 11, 10, 8, 8
18, 14, 11, 9, 9, 8
18, 14, 10, 10, 9, 8
18, 14, 10, 9, 9, 9
18, 13, 13, 10, 8, 8
18, 13, 13, 9, 9, 8
18, 13, 12, 11, 8, 8
18, 13, 12, 10, 9, 8
18, 13, 12, 9, 9, 9
18, 13, 11, 11, 9, 8
18, 13, 11, 10, 10, 8
18, 13, 11, 10, 9, 9
18, 13, 10, 10, 10, 9
18, 12, 12, 12, 8, 8
18, 12, 12, 11, 9, 8
18, 12, 12, 10, 10, 8
18, 12, 12, 10, 9, 9
18, 12, 11, 11, 10, 8
18, 12, 11, 11, 9, 9
18, 12, 11, 10, 10, 9
18, 12, 10, 10, 10, 10
18, 11, 11, 11, 11, 8
18, 11, 11, 11, 10, 9
18, 11, 11, 10, 10, 10
17, 17, 8, 8, 8, 8
17, 16, 12, 8, 8, 8
17, 16, 11, 9, 8, 8
17, 16, 10, 10, 8, 8
17, 16, 10, 9, 9, 8
17, 16, 9, 9, 9, 9
17, 15, 14, 8, 8, 8
17, 15, 13, 10, 8, 8
17, 15, 13, 9, 9, 8
17, 15, 12, 11, 8, 8
17, 15, 12, 10, 9, 8
17, 15, 12, 9, 9, 9
17, 15, 11, 11, 9, 8
17, 15, 11, 10, 10, 8
17, 15, 11, 10, 9, 9
17, 15, 10, 10, 10, 9
17, 14, 14, 10, 8, 8
17, 14, 14, 9, 9, 8
17, 14, 13, 12, 8, 8
17, 14, 13, 11, 9, 8
17, 14, 13, 10, 10, 8
17, 14, 13, 10, 9, 9
17, 14, 12, 12, 9, 8
17, 14, 12, 11, 10, 8
17, 14, 12, 11, 9, 9
17, 14, 12, 10, 10, 9
17, 14, 11, 11, 11, 8
17, 14, 11, 11, 10, 9
17, 14, 11, 10, 10, 10
17, 13, 13, 13, 9, 8
17, 13, 13, 12, 10, 8
17, 13, 13, 12, 9, 9
17, 13, 13, 11, 11, 8
17, 13, 13, 11, 10, 9
17, 13, 13, 10, 10, 10
17, 13, 12, 12, 11, 8
17, 13, 12, 12, 10, 9
17, 13, 12, 11, 11, 9
17, 13, 12, 11, 10, 10
17, 13, 11, 11, 11, 10
17, 12, 12, 12, 12, 8
17, 12, 12, 12, 11, 9
17, 12, 12, 12, 10, 10
17, 12, 12, 11, 11, 10
17, 12, 11, 11, 11, 11
16, 16, 14, 9, 8, 8
16, 16, 13, 11, 8, 8
16, 16, 13, 10, 9, 8
16, 16, 13, 9, 9, 9
16, 16, 12, 12, 8, 8
16, 16, 12, 11, 9, 8
16, 16, 12, 10, 10, 8
16, 16, 12, 10, 9, 9
16, 16, 11, 11, 10, 8
16, 16, 11, 11, 9, 9
16, 16, 11, 10, 10, 9
16, 16, 10, 10, 10, 10
16, 15, 15, 10, 8, 8
16, 15, 15, 9, 9, 8
16, 15, 14, 12, 8, 8
16, 15, 14, 11, 9, 8
16, 15, 14, 10, 10, 8
16, 15, 14, 10, 9, 9
16, 15, 13, 13, 9, 8
16, 15, 13, 12, 10, 8
16, 15, 13, 12, 9, 9
16, 15, 13, 11, 11, 8
16, 15, 13, 11, 10, 9
16, 15, 13, 10, 10, 10
16, 15, 12, 12, 11, 8
16, 15, 12, 12, 10, 9
16, 15, 12, 11, 11, 9
16, 15, 12, 11, 10, 10
16, 15, 11, 11, 11, 10
16, 14, 14, 13, 9, 8
16, 14, 14, 12, 10, 8
16, 14, 14, 12, 9, 9
16, 14, 14, 11, 11, 8
16, 14, 14, 11, 10, 9
16, 14, 14, 10, 10, 10
16, 14, 13, 13, 11, 8
16, 14, 13, 13, 10, 9
16, 14, 13, 12, 12, 8
16, 14, 13, 12, 11, 9
16, 14, 13, 12, 10, 10
16, 14, 13, 11, 11, 10
16, 14, 12, 12, 12, 9
16, 14, 12, 12, 11, 10
16, 14, 12, 11, 11, 11
16, 13, 13, 13, 13, 8
16, 13, 13, 13, 12, 9
16, 13, 13, 13, 11, 10
16, 13, 13, 12, 12, 10
16, 13, 13, 12, 11, 11
16, 13, 12, 12, 12, 11
16, 12, 12, 12, 12, 12
15, 15, 15, 13, 8, 8
15, 15, 15, 12, 9, 8
15, 15, 15, 11, 10, 8
15, 15, 15, 11, 9, 9
15, 15, 15, 10, 10, 9
15, 15, 14, 14, 8, 8
15, 15, 14, 13, 10, 8
15, 15, 14, 13, 9, 9
15, 15, 14, 12, 11, 8
15, 15, 14, 12, 10, 9
15, 15, 14, 11, 11, 9
15, 15, 14, 11, 10, 10
15, 15, 13, 13, 12, 8
15, 15, 13, 13, 11, 9
15, 15, 13, 13, 10, 10
15, 15, 13, 12, 12, 9
15, 15, 13, 12, 11, 10
15, 15, 13, 11, 11, 11
15, 15, 12, 12, 12, 10
15, 15, 12, 12, 11, 11
15, 14, 14, 14, 10, 8
15, 14, 14, 14, 9, 9
15, 14, 14, 13, 12, 8
15, 14, 14, 13, 11, 9
15, 14, 14, 13, 10, 10
15, 14, 14, 12, 12, 9
15, 14, 14, 12, 11, 10
15, 14, 14, 11, 11, 11
15, 14, 13, 13, 13, 9
15, 14, 13, 13, 12, 10
15, 14, 13, 13, 11, 11
15, 14, 13, 12, 12, 11
15, 14, 12, 12, 12, 12
15, 13, 13, 13, 13, 11
15, 13, 13, 13, 12, 12
14, 14, 14, 14, 12, 8
14, 14, 14, 14, 11, 9
14, 14, 14, 14, 10, 10
14, 14, 14, 13, 13, 9
14, 14, 14, 13, 12, 10
14, 14, 14, 13, 11, 11
14, 14, 14, 12, 12, 11
14, 14, 13, 13, 13, 11
14, 14, 13, 13, 12, 12
14, 13, 13, 13, 13, 13

 

[BoldItalic]

It gets interesting if you consider, not the ability scores themselves, but the resulting set of modifiers. Odd-numbered scores are "wasteful" in the sense that you could spend one or two fewer point and still get the same modifier, and then you might as well have used the points saved to boost a different ability. The question arises: can you arrange to get all your ability scores even?

Turns out there are only three combinations possible:

14,14,14,10,10,10
14,14,14,12,10,8
14,12,12,12,12,12​

Now, if you allow for racial bonuses the picture changes. For Humans you would want to point-buy six odd-numbered abilities, so that
after the blanket +1 to everything, they all end up even. Turns out it can't be done. You can't point-buy a standard Human with all even scores!

For Variant Humans, you would want two odd scores and four even; that's much easier but you have to include either one or three 14's (if you have three, there are still four possible combinations). The standard array does this, incidentally; it has one 14 and just two odd scores (13 and 15).

For other races (after allowing for subraces), you would want one odd and five evens. Turns out there are only seven ways of doing this:

15,14,14,12,8,8
15,14,14,10,10,8
15,12,12,12,12,10
14,14,13,12,12,8
14,14,13,12,10,10
14,14,12,12,12,9
14,14,12,12,11,10​

 

[Oofta]

It gets interesting if you consider, not the ability scores themselves, but the resulting set of modifiers. Odd-numbered scores are "wasteful" in the sense that you could spend one or two fewer point and still get the same modifier, and then you might as well have used the points saved to boost a different ability. The question arises: can you arrange to get all your ability scores even?

Turns out there are only three combinations possible:

14,14,14,10,10,10
14,14,14,12,10,8
14,12,12,12,12,12​

Now, if you allow for racial bonuses the picture changes. For Humans you would want to point-buy six odd-numbered abilities, so that
after the blanket +1 to everything, they all end up even. Turns out it can't be done. You can't point-buy a standard Human with all even scores!

For Variant Humans, you would want two odd scores and four even; that's much easier but you have to include either one or three 14's (if you have three, there are still four possible combinations). The standard array does this, incidentally; it has one 14 and just two odd scores (13 and 15).

For other races (after allowing for subraces), you would want one odd and five evens. Turns out there are only seven ways of doing this:

15,14,14,12,8,8
15,14,14,10,10,8
15,12,12,12,12,10
14,14,13,12,12,8
14,14,13,12,10,10
14,14,12,12,12,9
14,14,12,12,11,10​

Odd ability scores may not be wasteful if you plan on specific feats, or if you add 1 to two ability scores at some point.

But yes, it's interesting that out at 1st level there are only 3 and I've probably used them all at one time or other without realizing it.