Probability problems (Permutations, Combinations, law of inclusion and exclusion)

Ugher

0

Thank you. This is excellent. Can you explain this trivial answer I came across ? If the card deck (52 cards) is shuffled, what is the chance that the entire suit of hearts is together in the deck ? The answer states (40!)(13!)/(52!) but why is it 40 and not 39 ? Since there are 52 cards and 13 cards in a suit it should be (39!)(13!)/(52!), no ?

• Mathe

  0

  The 13 heart cards could be together starting position 1 or 2 or 3 or position 40. In other words, consider all the possible placements in which the hearts can be together. You must multiply by that number (40), making 39! into 40!. A tip would be appreciated!

Ugher

0

I will tip. But I still don't quite understand why a sequence of 13 (suit of hearts, let's call it a "chunk") must start at 1 or 2 or 3 or 40. I would understand if you said that they must start at any position that has atleast 13 spots left (52-13) is 39 and not 40. I still don't get it.

• Mathe

  0

  If they chunk is together, we have too choose where to place it among the 52 cards. There are 40 places we can put the chunk together.

Ugher

0

I dont understand where the 40 comes from

• Mathe

  0

  The chunk can go in one of 40 places. Consider 5 cards total and a chunk of size two. Where are you placing the chunk? At they very beginning, in second place or in third place?

Ugher

0

I still don't get it. But I tipped you for good work regardless.

• Ugher

  0

  can I ask you a direct question ? I need to have my test reviewed and corrected, and I liked the style of your solutions. It's 5 questions and they are pretty short but I need you to type out a clear solution and point out what I did wrong

• Mathe

  0

  Yes you can. I can read it and begin reviewing it in an hour. The system allows for direct questions.

Ugher

0

alright I will post right now

Ugher

0

Thank you, I accepted the anwer, I will ask maybe 2-3 follow up questions later.