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1 Answer

19C5= 19! / [(19-5) ! 5 !]

The above is just an identity.

The lhs is a short way of saying "The number of combinations of 19 objects, taken 5 at a time.

The rhs is a mathematical expression giving that numerical value, and where nCr = n! / [(n-r)! * r!]

19! / [(19-5) ! 5 !] = 

19! / [(14) ! 5 !] =   (divide above and below by 14!)

[19*18*17*16*15] / [5!] =   (expand 5!)

[19*18*17*16*15] / [5*4*3*2*1] =    (cancel common factors)

[19*18*17*2] / [1] =       (evaluate)

342 * 34 = 11,628

Answer: 11,628

 

by Level 11 User (80.5k points)

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