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Counting problem (aabbcccdddd)

  1. Apr 1, 2005 #1
    hi everyone....
    how many arrangements of this word "aabbcccdddd" is possible if we only use 3 of them? I know if we could use all of them it would just be 11!/(2!2!3!4!), but what if we only use 3? :confused:

    Thanks in advance
  2. jcsd
  3. Apr 1, 2005 #2
    I assume you mean 3 letters in the arrangement. First count the number of ways to permute using 1 letter of each, then in addition to that count the number of ways to permute using 1 of one letter and 2 of another, and then add 2 for the arrangements ccc and ddd.
  4. Apr 1, 2005 #3
    ok..thanks...so the answer would be 52?
  5. Apr 1, 2005 #4
    Not quite what I got--maybe you added wrong at the end?
  6. Apr 2, 2005 #5
    umm...i tried it again...i got 62 (checked it 3 times!)
  7. Apr 2, 2005 #6
    Yep, 62 is what I got. You said 52 the other time.
  8. Apr 2, 2005 #7
    thanks a lot
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