from BruceZ in the probability forum:
[ QUOTE ]
For at least 1, we can get the exact answer from the
inclusion-exclusion principle similar to
these problems to get:
6*12/C(52,2) -
C(6,2)*12*7/C(52,2)/C(50,2) +
C(6,3)*12*(6*2+1*6)/C(52,2)/C(50,2)/C(48,2) -
C(6,4)*12*(6*2+1*6)/C(52,2)/C(50,2)/C(48,2)/C(46,2)
=~5.35%
For exactly 1, we make the following modification:
6*12/C(52,2) -
2*C(6,2)*12*7/C(52,2)/C(50,2) +
3*C(6,3)*12*(6*2+1*6)/C(52,2)/C(50,2)/C(48,2) -
4*C(6,4)*12*(6*2+1*6)/C(52,2)/C(50,2)/C(48,2)/C(46,2)
=~ 5.28%
[/ QUOTE ]