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Expert: - 9/16/2008


Question
say you have the following formula 46!/[6!*(46-6)!] aka
46 C 6. what would the answer be first off? and secondly would the some of the factorials of the numerator (ie. 1-40) cancel with the factorials of 40! in the denominator.
  And i apologize if my terminology is incorrect i am not a teacher or even taking the subject just trying to figure out how many possible combinations there are if you have 45 options and you have to choose at least 6 in every combination.

Answer
The answer would be computed as 45*45*44*43*42*41/(6*5*4*3*2*1).
46! isn't computed on calculators with out a power of 10 being displayed.  Even if they have that, it might be outside the range.

If you only look at 10!, you get 3,628,800.  The number 11 to 30 would each add at least one digit, so it's at least some number times 10^27.

It is easy to right them that way, but easier to cancel digits when computing.  On a computer program, I would multiply 1 in a for loop by (46-i)/(6-i) where i went from 0 to 5 (1-1 to 6-1).

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