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Homework Help: Lottery Picks

  1. Sep 29, 2011 #1
    In a lottery , 6 distinct numbers are selected at random from a set {1.........50} and designated as a winning number. The player picks six numbers beforehand hoping to include as many numbers as possible. Find the probability that the user picks k winning numbers for k=1,2..,6

    So my one concern is that my answers dont sum to 1

    for K=0 I have (44C6)/(50C6)
    for K=1 I have (44C5)/(50C6)
    for K=2 I have (44C4)/(50C6)
    for K=3 I have (44C3)/(50C6)
    for K=4 I have (44C2)/(50C6)
    for K=5 I have (44C1)/(50C6)
    for K=6 I have (44C0)/(50C6)

    My reasoning is that for k=0 you didnt pick any of the six numbers so you must have chosen 6 of the 44 remaining
    and used similiar reasoning for k=1...6

    My question is are my answers right or did i miss something ?
    Last edited: Sep 29, 2011
  2. jcsd
  3. Sep 29, 2011 #2
    Let's consider the case K=2, for example. Let's call your chosen 6 numbers "winners" and the remaining 44 numbers "losers". 44C4 is the number of ways you can pick the 4 losers-- there you are right.

    But how many ways are there for you to pick the 2 winners?
  4. Sep 29, 2011 #3
    There are 6C2. So there should be 6C2 * 44C4

    Thanks that fixed it
    Last edited: Sep 29, 2011
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