No disrespect, but those are the odds if we have 5 numbers each pick. Since we only have three per pick, the math works like this (I didn't do the math, a friend of mine who wrote a book on statistics did):
How many ways can you draw three numbers from 70?
N = 70! / (70-3)!/3! = 54,740
How many valid three number combinations can a set of five numbers contain?
M = 5! / (5-3)! / 3! = 10
(If the five numbers were 1-2-3-4-5, valid combinations would be: 5-4-3, 5-4-2, 5-4-1, 5-3-2, 5-3-1, 5-2-1, 4-3-2, 4-3-1, 4-2-1, 3-2-1)
So the odds of drawing one of the 10 sets of valid triplets from 54,740 is:
1:5,474.
But wait...maybe his math is wrong. Since we first have to reduce the subset of numbers to the five picked (not 3), it would be 70! / (70-5)!/5! , which is 12103014. There are still 10 ways to hit those three...which would make it 1:1210301.4
I'll have to have him check it out again, but it's one of the two.