" (A) "quad nP_(r)=n*n-1P_(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)

11. Prove that nP_(r)=n(n-1)P_(r-1)

Show that ^(^^)nP_(r)=(n-r+1)^(n)P_(r-1)

If nC_(r)=nC_(r-1) and nP_(r)=nP_(r+1), then the value of n is

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

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

if nP_(r)=nP_(r+1) and nC_(r)=nC_(r-1) then value of (n+r) is equal to

P(n,r)+P(n-1,r-1)=

If ""^(nP_(r)=""^(n)P_(r+1) and ""^(n)C_(r)=""^(n)C_(r-1) find n and r.