Question

if 5P(n,3) = 4P(n,1+3) then n is

Answer 1

→5 P (n,3) = 4 P [n,(1+3)]

→ 5 P (n,3) = 4 P(n,4)

→As P(n,r)= $\frac{n!}{(n-r)!}$

→5 × $\frac{n!}{(n-3)!} = 4 \times \frac{n!}{(n-4)!}$

Cancelling n! from numerator, and (n-3)!= (n-3)(n-4)! , so cancelling (n-4)! from denominator we get

$\frac{5}{n-3} =4$

→5= 4(n-3)

→5 = 4n -12

→5+12 = 4 n

→4 n= 17

→n= 17/4, which is impossible because n can't be a rational number.