Let $\lambda\leq\kappa$ be infinite cardinals. Then $| \{X\subset \kappa | |X|=\lambda \} | = \kappa^{\lambda} $
$\leq$ part is trivial, but I don't know how to prove the other part. I used transfinite induction on $\lambda$ but it didn't work to me. Can I have any hint for this?
Thanks in advance
