How many sixcard hands can be chosen from exactly 2 suits of

How many six-card hands can be chosen from exactly 2 suits of an ordinary 52-card deck? (there are 4 suits clubs, diamonds, hearts and spades) Find a numerical answer and show your work.

Solution

in six-card hands can be chosen from exactly 2 suits of an ordinary 52-card deck? (there are 4 suits clubs, diamonds, hearts and spades)

remain:2 suits of an ordinary 52-card deck is

            52c2-13c₁-13c₁-13c₁-13c₁.

            1326-(13+13+13+13)=1274