Find r if (i) `^5P_r=2^6P_(r-1)` (ii) `^5P_r=^6P_(r-1)`

Find r if (i) .^(5)P_(r) = 2 .^(6)P_(r-1) (ii) .^(5)P_(r) =^(6)P_(r-1) .

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

Find r, if 5^(4)P_(r)=6^(5)P_(r-1)

Find 'r' if : (i) ""^(5)P_(r )= ""^(6)P_(r-1) (ii) 5""^(4)P_(r )=6""^(5)P_(r-1) (iii) ""^(5)P_(r )=2""^(6)P_(r-1) (iv) ""^(10)P_(r+1): ""^(11)P_(r )=30 :11 .

Find r if 4.P(6,r)=P(6,r+1)

Find 'r' when : (i) ""^(10)P_(r )=2 ""^(9)P_(r ) (ii) ""^(11)P_(r )= ""^(12)P_(r-1) .

Prove that: (i) ""^(n)P_(n)=""^(n)P_(n-1) " (ii) "^(n)P_(r)=n* ""^(n-1)P_(r-1) " (iii) "^(n-1)P_(r)+r* ""^(n-1)P_(r-1)=""^(n)P_(r)