5 A's and no B's - [tex] 1 [/tex]
5 A's and 1 B - [tex] \dfrac{6!}{5!}=6 [/tex]
5 A's and 2 B's - [tex] \dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21 [/tex]
5 A's and 3 B's - [tex] \dfrac{8!}{5!3!}=\dfrac{6\cdot7\cdot8}{2\cdot3}=56 [/tex]
[tex]56+21+6+1=84 [/tex]
