There are $3$ men, $2$ women and $4$ children. If $4$ persons are selected then which of the following is/are true?

If alphabets of word RAKESH are written in given boxes, then probability that no row remains empty is

Let $H_1, H_2, H_3,..., H_n$ be mutually exclusive and exhaustive events with $P\left(H_i\right)>0, i=1, 2, 3,..., n.$

Let $E$ be any other even with $0<P\left(E\right)<1.$

STATEMENT-$1 :$ $P\left(H_i|E\right)>P\left(E|H_i\right)·P\left(H_i\right)$ for $i=1, 2, 3,..., n.$

and 

STATEMENT-$2 :$ $\sum _{i=1}^{n}P\left(H_i\right)=1.$