filtering - Using select to pick out elements of nested lists in an odd way

Suppose I have a nested list such as,

{{{A, B}, {A, D}}, {{C, D}, {A, A}, {H, A}}, {{A, H}}}

Where the elements of interest are,

{{A, B}, {A, D}}


{{C, D}, {A, A}, {H, A}}

{{A, H}}

How would I use select to pick up only elements that contain two or more As in the first part of their sub-elements. In this example I would want the following as an output,

{{A,B},{A,D}}

Answer

list = {{{a, b}, {a, d}}, {{c, d}, {a, a}, {h, a}}, {{a, h}}}

Pick[list, Count[#[[All, 1]], a] >= 2 & /@ list]

or

Select[list, Count[#[[All, 1]], a] >= 2 &]

or

Cases[list, _?(Count[#[[All, 1]], a] >= 2 &)]

or

DeleteCases[list, _?(! Count[#[[All, 1]], a] >= 2 &)]

all give

{{{a, b}, {a, d}}}