problem 232 mathcounts

Mathematics
Tutor: None Selected Time limit: 1 Day

In a beauty contest, 51 contestants must be narrowed down to a first-,second- and third-place finalist. In how many ways can three finalists be chosen?

Oct 5th, 2014

51C3= 51!/(51-3)!3!

         = 51!/48!*3!

         = 51*50*49*48!/48!*3*2*1

         = 51*50*49/3*2*1

         = 20825

Oct 5th, 2014

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