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factorial expressions
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factorial expressions

by Barbara Scott
(Baton Rouge, La)











































Evaluate the following factorial expression:

12!6!
_____
14!8!

Evaluating each factorial is not necessary.

Some of the factors in the numerator cancel corresponding factors in the denominator.

Comments for factorial expressions

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Jan 10, 2011
Factorial Division
by: Staff

The question:
by Barbara Scott
(Baton Rouge, La)


12!6!
_____
14!8!





The answer:

12!6!
_____
14!8!

Although it is not necessary, I have written out the factorials.

12! = 12 x 11x 10 x 9 x 8 x 7 x6 x 5 x 4 x 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x 1
14! = 14 x 13 x 12 x 11x 10 x 9 x 8 x 7 x6 x 5 x 4 x 3 x 2 x 1
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1


Evaluating each factorial is not necessary.

For your specific problem, most of the factors in the numerator cancel with corresponding factors in the denominator.

12!6!
_____
14!8!




(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)( 6 x 5 x 4 x 3 x 2 x 1)
_______________________________________________________
(14 x 13 x 12 x 11x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

On the left, the 12 x 11x 10 x 9 x 8 x 7 x6 x 5 x 4 x 3 x 2 in the numerator cancels with the 12 x 11x 10 x 9 x 8 x 7 x6 x 5 x 4 x 3 x 2 in the denominator.

On the right, the 6 x 5 x 4 x 3 x 2 x 1 in the numerator cancels with the 6 x 5 x 4 x 3 x 2 x 1 in the denominator.

After canceling those factors, the problem is greatly simplified. The result is:


(1)( 1)
__________________
(14 x 13)( 8 x 7 )


1
___________
(182)( 56 )


1
_____
10192

= 0.00009811617



Thanks for writing.


Staff
www.solving-math-problems.com


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