Bad Question

We were doing a bit of an assessment review and I threw in this question. Please note that I did not refer to the name of card game that the 4 friends were playing - it could have been just about anything:

As I was going around looking at what the kids were doing, it suddenly dawned on me that this was a really bad question, quite apart from the fact that this deck seemed to have three 9 of diamonds.

Each of the "hands" had exactly the same chance of happening. And I had asked about the chances of getting each particular hand.

Bad question.

According to a reliable source, there are 2 598 960 possible hands that you can be dealt in 5 card poker. So each of the hands illustrated above has the exact same chance of happening, that is 1:2598960.

I had given too much information. I should have referred instead to "one pair", "all 5 cards diamonds", "four 9's" etc.

Incidentally, there is a greater chance of getting dealt a pair (2860 possible combinations) than getting dealt nothing (1277 possible combinations). Who would have thought?

Hmm, good thing I don't play cards for money...