Rank the following five-card hands in order of increasing probability:

VIDEO TRANSCRIPT

This is Giancoli answers with Mr. Dychko. In the five-card hand it doesn't matter what order you hold the cards in your hand it's still the same hands. So, whether you have your six of hearts first and then the eight of diamond second or eight of diamonds first and six of hearts second, it's the same macro-state. So, the number of micro-states corresponding to this hand is one, doesn't matter what order the arrange, you arrange the cards and so only one micro-state because every single card is totally specified, the six has to have the suit of hearts and in the eight is to diamonds and the queen of clubs and the three of hearts and the jack of spades. There is one micro-state for this macro-state and so that makes it the lowest probability possible hand here and the next lowest probability is the four aces and a king. There are four macro-states here because the suit of the King hasn't been specified so it could be a diamonds, heart, clubs or spades or so those are the four possibilities for this macro-state. So, there are four micro-states. With the next hand two Jacks, two queens and an ace, there is lots of micro-states because the Jacks could be of any of those four suits. The Queens could be any of those four suits and the ace could be of any of the four suits. Certainly more micro states than this hand and so that puts it down here with a higher probability. So, we're going from lowest to high probability here. And then with no duplicate values clearly there are a huge number of micro-states for that because you can have, you know, you have four different suits for this one and four different suits for the next one and four different suits for the next one and four different suits for the next one and so on. So that makes this the highest probability, lots of micro-states.