Graphs and Degrees · Challenge problem

How many of these are degree sequences of simple graphs? $(5,5,4,3,2,2,1)$, $(5,5,5,3,3,2,1)$, $(6,5,4,3,2,2,2)$, $(4,4,4,4,2,2,2)$, $(6,6,4,2,2,2,2)$.