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  A teacher has made ten statements for a True-False test.     

  Four statements are true and six are false.     

  How many distinct answer keys could the     

 

  The four (true) answers can be arranged ₁₀C₄  =  210 ways.     

  The six (false) answers can be arranged ₁₀C₆  =  210 ways.     

 

  For each way the true answers can be arranged,     

  the false answers can be arrangeddd 210 ways.     

 

  So there could be 210 x 210 =  44,100 answer keys.     

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