We have a total of n-1 persons $(P1,P2,...Pn-1)$ and n houses $(H1, H2, Hn)$.

FInd the number of ways for n=6 such that each person visits only 1 house and the following conditions are satisfied:

$1.$ Each person visits a different house

$2.$ Person Pi can’t visit House $H_i$

$3.$ P1 can’t visit House $H_n$