Background: If we have two DFAs, $M_1=(Q_1,,{}_1,q_1,F_1),$ which recognizes language $A_1,$ and $M_2=(Q_2,,{}_2,q_2,F_2),$ which recognizes language $A_2,$ we can construct a machine $M=(Q,,,q_0,F)$ that recognizes language $A_1{A}_2$ as follows:

$Q=Q_1{Q}_2$

For each $(r_1,r_2)inQ$ and each ain$,((r_1,r_2),a)=({}_1(r_1,a),{}_2(r_2,a))$

$q_0=(q_1,q_2)$

$F=F_1{F}_2$

Question: The following language is an intersection of two simpler languages. First construct DFAs for the simpler languages, then combine them using the construction described above in the background. $=\{a,b\},$

has at least three $a\text{'}$s and at least two $b\text{'}$s