Monday, June 27, 2011

A Counting Problem

How many terms are contained in (a + b + c)20 .


  1. 2^20 or 1048576 terms

  2. Er, should be 3^20, or 3486784401 terms.

  3. At least one. If a+b+c=1 then 1^20=1.

  4. 3^20 is the number of terms not simplified, i.e., it woulb be a lot of identical terms that wwe can add up.

    The answer is "combinations", where n=3; r=20. The order is not important and repetition is allowed.

    (n+r-1)!/r!(n-1)!= 231


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