Question

Find the value of r if P(56, r+6) : P(54, r+3) = 30800 : 1.

Answer 1

i) nPr = n!/(n - r)! 
So, 56P(r+6) = 56!/(50 - r)! and 54P(r+3) = 54!/(51 - r)! 

ii) Hence, the ratio reduces to: {56!/(50 - r)!}*{(51 - r)!/54!)} 

= {56*55*54!/(50 - r)!}*{(51 - r)*(50 - r)!/54!} = 56*55*(51 - r) = 30800 

==> 51 - r = 30800/56*55 = 10 

Hence r = 51 - 10 = 41.