Find r if `"^(5)P_r = 2 .^(6)P_(r-1)`

Find r if "^5P_r =2 "^6P_(r-1) .

Find r if "^5P_r = "^6P_(r-1) .

Find r if : "^10P_r= 2^9P_r .

Find r if : ^5P_r= "^6P_(r-1) .

Find the value of r if 5. ^4P_r= 6. "^5P_(r-1) .

Find r if : ^10P_(r+1): "^11 P_(r)= 30:11 .

Prove that : ^nP_r= "^(n-1)P_r+r ^(n-1)P_(r-1) , for all natural numbers n and r for which the symbols are defined.

Find r if : P(11,r) = P(12,r-1)

Find the value of r, if (i) .^(11)P_(r)=990 (ii) .^(8)P_(5)+5*^(8)P_(4)=^(9)P_(r)