Hey Guys,
Sorry for Random Question Need help with Math/Confirm

3 Players left in Tournament Final table

All 3 Players have hole cards J9o

Flop is 7 8 10,

I'm Not concerned with suits, just want to know what the odds are that 3 players in 3 player table have same hand and Flop the straight?

I got like 1:33B Seems High.

There are C(52,5) = 2,598,960 ways to deal one set of pocket cards and a flop, 10,240 (ten different possible highest cards, from 5 to A, 4^5 ways of arranging the suits for each one) of them make a straight (that includes 40 straight flushes, ten different possible highest cards, 4 suits). So the chance of that is 1 in 254.

Given that happens, there are C(47,2) = 1,081 ways to deal a second set of pocket cards. Nine of them will match the two ranks in the first set (three possibilities for each of the two ranks). Given that happens, there are C(45,2) = 990 ways to deal the third set of pocket cards, four of which will match the ranks.

Put it all together and you get 10,240*9*4 / (2,598,960*1,081*990) = 368,640 / 2,781,381,002,400 or about 1 in 7.5 million. That's pretty uncommon, but if you play a lot of poker things of about equal probability will happen now and again.