What is the probability of being dealt four cards from a shuffled deck of 52 such that no card is of the same suit? That is four different suits.

Given that, what is the probability for getting that result 6 times in a row from the same deck? Cards are not returned as they are dealt.

For the first question I come up with 10.55%. {13^4/52*51*50*49}4!
I'm not sure about the second question.


Thanks,

Larry

After the first card is dealt you have 39/51 chances to avoid the same suit. Once that has succeeded you have 26/50 to avoid both those suits. Finally 13/49 to avoid the three suits dealt. Multiply these probabilities. (Same result as yours, which it should be.)

Only 12 of each suit left and 48 cards. The next five rounds are analogous, so you can use your formula you posted or do the following:

The next run you can again deal any suit. 36/47 cards doesn't match it. Then 24/46 doesn't match those two. 12/45 does not match the three dealt. Multiply these probabilities with the previous.

Only 11 cards of each suit and 44 cards left.

Etc.

/Tomas

Thanks Tomas. That was very clear and helpful.

Larry