## Wednesday, May 13, 2009

### Permutative and Combinatory BOB

I think I'll start off my bob by answering the poker questions. And I would like to extend my gratitude to Dion and Aldrin and Physics, where the 3 of us did this (Not because we weren't working or nothing).

We already the the Royal Flush, so I' not going to bother with that one.

To get the combinations of Straight Flushes you need to do 10 Choose 1 times 4 Choose 1 minus 4 Choose 1. 10 Choose 1 determines the number of different straights you have without repetition, you multiply by 4 Choose 1 because of the suits ( 4 suits, 4 choices), then you subtract by 4 Choose 1 because you eliminate the royal flush group.

To get the combinations of Four of a Kind you need to do 13 Choose 1 times 4 Choose 4 times 48 Choose 1. You use 13 Choose 1 because every single card in a deck has the chance of becoming a four of a kind and you only have 13 different types of cards. You multiply by 4 Choose 4 because you have to obtain all the suits to get the 4 cards. You multiply by 48 Choose 1 because you have 48 cards left and any of those cards can be your last card.

To get the combinations of Full House you need to do 13 Choose 1 times 4 Choose 3 times 12 Choose 1 times 4 Choose 2. You use 13 Choose 1 because every single card in a deck has the chance of becoming a three of a kind and you only have 13 different types of cards. You multiply by 4 Choose 3 because you have to obtain 3 suits to get the the triple. You multiply by 12 Choose 1 because you need a pair and you cant make a pair from the triple you already have, so you have only 12 different number pairs. You multiply by 4 Choose 2 because you want 2 of the suits out of the 4 and it doesn't matter what order it is.

To get the combinations of Flushes you need to do 13 Choose 5 times 4 Choose 1 minus 10 Choose 1 times 4 Choose 1. 13 Choose 5 picks any 5 different numbers out of the 13, then multiply by 4 Choose 1 because of the suits ( 4 suits, 4 choices), then you subtract by 10 Choose 1 times 4 Choose 1 because you eliminate the the straight flush and the royal flush group, so it'sall good.

To get the combinations of Straights you need to do 10 Choose 1 times 4 Choose 1 to the exponent 5 minus 10 Choose 1 times 4 Choose 1. 10 Choose 1 picks any 1 of the 10 possible straight combinations, then multiply by 4 Choose 1 to the exponent 5 because of the suits ( 4 suits, 4 choices) and every single cards' suit doesn't matter so that's why the exponent 5, then you subtract by 10 Choose 1 times 4 Choose 1 because you eliminate the the straight flush and the royal flush group, so it'sall good, again.

To get the combinations of Three of a Kind you need to do 13 Choose 1 times 4 Choose 3 times 12 Choose 2 times 4 Choose 1 squared. You use 13 Choose 1 because every single card in a deck has the chance of becoming a three of a kind and you only have 13 different types of cards. You multiply by 4 Choose 3 because you have to obtain 3 suits to get the the triple. You multiply by 12 Choose 2 because you need 2 different cards that aren't the card you previously chose and the cards you pick can't be a pair. You multiply by 4 Choose 1 squared because the suits of the 2 cards you chose makes no difference.

To get the combinations of 2 Pairs you need to do 13 Choose 2 times 4 Choose 2 squared times 11 Choose 1 times 4 Choose 1. 13 Choose 2 picks 2 different pairs out of the 13 you have, then multiply by 4 Choose 2 squared because of the suits for both pairs, then you multiply by 11 Choose 1 because the last card can be any number except the 2 pairs that you have and you multiply by 4 Choose 1 because suit doesn't matter again.

To get the combinations of 1 Pair you need to do 13 Choose 1 times 4 Choose 2 times 12 Choose 3 times 4 Choose 1 cubed. 13 Choose 1 chooses the 1 pair out of the 13 you need, then multiply by 4 Choose 2 because of the suits for the pair, then you multiply by 12 Choose 3 because the last 3 cards can be any 3 different numbers from each other and from the pair you have chosen and you multiply by 4 Choose 1 cubed because suit of the last 3 cards doesn't matter again, again.

*note: If you haven't noticed by now, most of this is repetitive because I'm copying and pasting to "try" to save time to do my english project, oh and this next question is pretty interesting, needed to look it up to understand.

To get the combinations of No Pair you need to do (13 Choose 5 minus 10) times (4 Choose 1 5th'd minus 4). (13 Choose 5 minus 10) chooses 5 different numbed/face cards and you subtract 10 for the 10 different possible straights and you multiply by (4 Choose 1 5th'd minus 4) because the suit doesn't matter for each card, but you still have to disclude the 4 possible flushes.

So, I'll let you guys multiply those numbers out because I probably would miss a zero or space or something like that and I'll continue my BOB.

We learnt about combinations first, which is pretty much is how many ways can you do 2 things. For example; you have 2 coins, how many different outcomes can you have? The answer is 4 because the first one can come out 2! ways or 2 and the second one can also come out 2 ! ways or 2, so you just multiply them.

Then we learnt about non distinguishable objects, which it discludes repetitions of the same thing. For example; how many different ways can you make the word moo using all the letters? Like Mr. K said "42" and "both of the "o's" are non-distinguishable objects, so you need to use the choose formula. Which is n!/k! where n is how many words you have and k is how many ways you can arrange your non distinguishable objects you have.

And I must be really slow because when I started BOBing only 2 Bobs were already made and now there's like 30ish. So i think i should end it now and get on to my English. Good luck on the pre-test tomorrow.

Thanks Aldrin for the error.