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Combinatorics question

  1. Nov 5, 2009 #1
    given the numbers 1 2 3 4 5 6 7, how many even 3 digit numbers can be made from these 7 digits
    a) if each number can only be used once
    b) if each number can be rused


    for b) what i did was:
    for the first digit i have 7 options, for the second still 7, since i can reuse, and for the 3rd only 3 since the last digit needs to be even

    7*7*3=147

    but for a) i am stuck, for the first i have 7 options, for the second i have 6 since i have used one already, but how many do i have for the final digit, i would think 3, but what if the 1st 2 were also even, then i only have 1 even left? the correct answer is 90 but i cannnot get it
     
  2. jcsd
  3. Nov 6, 2009 #2

    lanedance

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    try counting from the even digit first... ie pick the smallest digit first then so on...
     
  4. Nov 6, 2009 #3
    nice, thanks

    3*5*6
     
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