" सिदs कीजिए कि "nP_(r)=n.^(n-1)P_(r-1)

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

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

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

What is ""^(n-1)P_(r )+ ""^(n-1)P_(r-1) ?

If show that "^(n-1)P_r = (n-r).^(n-1)P_(r-1)

(n-1)P_(r)+r.(n-1)P_(n-1) is equal to

(n-1)P_(r)+r.n-1)P_(n-1) is equal to

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