What Are the Odds That a Given Cow Will Make It to the Super Bowl?

  66200000 / 17420000 * 20 = 76

This article is only true if every cow hide's resultant balls are sent to the exact same place. The superbowl could very well choose 76 different cowhide donors.

  76 / 66200000 = 1 / 871 052.6

If that were the case, the odds would be (go figure) about 20x better of being chosen.

I bet the true probability is somewhere in between

Is it just me or did they miscalculate the odds here by trying to tell a story? It seems the only things that matter are:

  # of cows slaughtered annually: 66.2M / 1.99 =  33,266,331.7 
  # of footballs made per cow: 20
  # of footballs used in the Super Bowl: 76
  # of cows required to make the SB balls: 76 / 20 = 3.8
  Odds a randomly slaughtered cow becomes a SB football = 33,266,331.7 / 3.8 = 1 in 8,754,297.82

What am I missing?

Related:

"... Thus there is a 1.8% chance that none of the molecules you are (still) holding in your lungs came from Caesar's last breath. And there is a 98.2% chance that at least one of the molecules in your lungs came from Caesar's last breath."

--John Allen Paulos, Innumeracy (1988) [1]

[1] http://econ161.berkeley.edu/movable_type/archives/001392.htm...