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Difficult Permutations Problem - two tables lots of people...


choked

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I'm having a lot of trouble making my answer look like the OA. Can someone help?

 

Here's the problem:

 

In how many different ways can 12 people be seated at two tables with one seating 7 and the other seating 5?

 

 

 

 

OA is 13,685,760, which, I think, comes from 12P5*4!*3!. Prime factorization of the OA yields 2^10*3^5*5*11, which I figured must look something like (12*11*10*9*8*4*4*3*3).

 

Anybody want to help me out with this problem?

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