Odds of overcards on flop

[Vertical Taco]

According to this Chart the chances of an overcard appearing on the flop when you hold TT is 70%.

Could someone show me how they arrived at these numbers? Show work plz.

[rufus]

It's a bit easier to work out no overcards, and subtract that from 1.

Of the remaining cards, there are 34 cards that are not over cards (2 tens, and 4 each of 2 through 9).

That means that there are 34 choose 3 flops that don't feature an overcard, and 50 choose 3 flops in total.

So the chance of no overcard is ((34*33*32)/6)/((50*49*48)/6)=(34*33*32)/(50*49*48)=35904/117600 - 30.5%.
So the chance of an overcard is 1-30.5%=69.5%.