Question

If $_{10} P _r = 5040$, find the value of $r$.

Answer 1

10Pr = 5040
10!/(10-r)! = 5040
10*9*8........(10-r)!/(10-r)!=5040
10*9*8.....(10-r+1) = 10*9*8*7
⇒(10-r+1) = 7
⇒11-r=7
⇒11-7 = r
⇒r = 4

Answer 2

10Pr = 5040
10! / (10-r)! = 10! / 6!
10-r = 6
r = 4