Question

Find the value of each of these quantities.
C(5,3)
C(8,8)
C(12,6)

Answer 1

`C^n_k= (n!)/((n-k)!c!) \\ \\C^5_3= (5!)/((5-3)!3!) = (5!)/(2!3!) = (5*4*3)/(3*2*1) =10 \\ \\C^8_8= (8!)/((8-8)!8!) = (8!)/(0!8!) = (8!)/(1*8!)=1 \\ \\C^(12)_6= (12!)/((12-6)!6!) = (12!)/(6!6!) = (12*11*10*9*8*7)/(6*5*4*3*2*1) =(11*3*4*7)/(1) =924`