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Counting math

  1. Apr 1, 2004 #1
    I have some questions about counting principles in mathematics:

    If I had standard deck of 52 playing cards, then

    a. How many ways can one draw a heart or a space?
    b. " " an ace or a king?
    c. " " a card numbered 2 through 10?
    d. " " a card numbered 2 through 10 or a king?

    I got these answers (using the addition rule of a disjoint union and the multiplication rule):

    a. Let A = cards that are hearts and B = cards that are spades.
    |A| + |B| = 13 + 13 = 26
    b. Let A = aces and B = kings
    |A| + |B| = 4 + 4 = 8
    c. Let A = {2, 3, 4, ... 10 belonging to hearts}, B = {2...10 belonging to spades}, C = {2...10 belonging to diamonds}, and D = {2...10 belonging to clubs}
    |A| + |B| + |C| + |D| = 9 + 9 + 9 + 9 = 36
    d. Take previous answer and add to 4 (Let E = kings):
    36 + |E| = 40

    Am I correct as far as using these rules? Thanks.
     
  2. jcsd
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