Odds of flopping no overcards while holding a big pair

[eastbay]

What are the odds of flopping no overcards while holding:

KK
QQ
JJ
TT
99

[Henke]

If we assume that we have no clue about the opponents cards, then there are 50 unseen cards. Let n be the number of overcards. The probability of the flop containing no overcards is then:
C(50-n,3)/C(50,3)

For KK, n=4 => 77.45% => 0.29:1
QQ, n=8 => 58.57% => 0.71:1
JJ, n=12 => 43.04% => 1.32:1
TT, n=16 => 30.53% => 2.28:1
99, n=20 => 20.71% => 3.83:1

[Louie Landale]

Please recalculate disallowing flops that contain your rank. I think that will be C(48-n,3)/C(50,3).

This number will represent the chances that you "like the flop": flop AJ4 is great for JJ.

- Louie

[Bozeman]

C(48-n,3)/C(50,3)+(1-48/50*47/49*46/48)

kk 79.3%
qq 62.2%
...

[Bozeman]

=C(48-n,3)/C(50,3)+(1-C(48,3)/C(50,3))

[Dr.Kimble]

KK 77.449
QQ 58.571
JJ 43.041
TT 30.531
99 20.714