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Math Help - Data Management Problem Help

  1. #1
    Junior Member Morphayne's Avatar
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    Exclamation Data Management Problem Help

    I know I may be asking too much on this one, but please hear me out. I'm taking a data management course in summer school, summer school is only 3 weeks long. So basically, I'm learn a large amount of material everyday for six hours, material that would normally take a semester(5 months) to cover. So, as you may imagine, the pacing of the course is very quick.

    So please sympathize with situation. I really need help with this problem.

    Problem:

    This is an organized counting problem.

    a) In how many ways could you choose two fives, one after the other, from a deck of cards?

    b) In how many ways could you choose a red five and a spade, one after the other?

    c) In how many ways could you choose a red five or a spade?

    d) In how many ways could you choose a red five or a heart?

    Answers:

    a)12
    b)26
    c)15
    d)14
    Last edited by Morphayne; July 17th 2008 at 04:11 PM.
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  2. #2
    Member
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    Quote Originally Posted by Morphayne View Post
    I know I may be asking too much on this one, but please hear me out. I'm taking a data management course in summer school, summer school is only 3 weeks long. So basically, I'm learn a large amount of material everyday for six hours, material that would normally take a semester(5 months) to cover. So, as you may imagine, the pacing of the course is very quick.

    So please sympathize with situation. I really need help with this problem.

    Problem:

    This is an organized counting problem.

    a) In how many ways could you choose two fives, one after the other, from a deck of cards?

    b) In how many ways could you choose a red five and a spade, one after the other?

    c) In how many ways could you choose a red five or a spade?

    d) In how many ways could you choose a red five or a heart?

    Answers:

    a)12
    b)26
    c)15
    d)14
    Ask your self are you picking with replacement and does order matter?
    1) No and Yes (although the wording "one after another" took me a second - I think they mean that it matters).

    Ok so you use combinations:

    You want to pick 2 cards from 4. Even though there are 52 cards, it doesn't matter for this. You want to know how many ways to pick from the set of 5's.

    {\mathbb{P}^4_2} = \frac{4!}{(4-2)!} = 12

    2) No and Yes

    You want to pick 1 from 2 cards (2 red 5's) and then pick 1 from 13 cards (13 spades)

    2*13 = 26

    Technically you could do
    {\mathbb{P}^2_1 * \mathbb{P}^{13}_1}
    but you get the same thing. It's just the more general approach.

    3) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or spade)?

    4) Hint: This question is really asking (since you are only picking 1 card) how many cards satisfy (either red 5 or heart)? (notice that these sets overlap).
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