Odds of picking QBs on two different teams that share the same bye week.

qbs

32 NFL teams
9 bye weeks, differing teams
Odds that both QBs (assume different teams) are bye on same week?

Team combinations: 992

Bye weeks:

Week 4
Arizona Cardinals, Cincinnati Bengals, Cleveland Browns, Denver Broncos, St. Louis Rams, Seattle Seahawks
= 6C2 = 15

Week 5 
Miami Dolphins, Oakland Raiders
= 2C2 = 1

Week 6
Kansas City Chiefs, New Orleans Saints
= 2C2 = 1

Week 7
Philadelphia Eagles, Tampa Bay Buccaneers
= 2C2 = 1

Week 8
New York Giants, San Francisco 49ers
= 2C2 = 1

Week 9
Atlanta Falcons, Buffalo Bills, Chicago Bears, Detroit Lions, Green Bay Packers, Tennessee Titans
= 6C2 = 15

Week 10
Houston Texans, Indianapolis Colts, Minnesota Vikings, New England Patriots, San Diego Chargers, Washington Redskins
= 6C2 = 15

Week 11
Baltimore Ravens, Dallas Cowboys, Jacksonville Jaguars, New York Jets
= 4C2 = 6

Week 12
Carolina Panthers, Pittsburgh Steelers
= 2C2 = 1

=> Total team combinations with intersecting bye weeks: 15 + 1 + 1 + 1 + 1 + 15 + 15 + 6 + 1 = 56

Odds of picking QBs on two different teams that share a bye week: 56/992 = 0.0565 = 5.56%