How many possible passwords with six to eight character long , each character is a letter or digit and each password must at least contains a digit ?

\begin{array}{l} L e t p_{6} = o f p a s s w o r d s o f s i x c h a r a c t e r s \\ p_{7} = o f p a s s w o r d s o f s e v e n c h a r a c t e r s \\ p_{8} = o f p a s s w o r d s o f e i g h t c h a r a c t e r s \\ U s i n g s u m r u l e t h e r e a r e p_{6} + p_{7} + p_{8} p a s s w o r d s . \\ p_{6} = (# o f a l l p o s s i p l e s t r i n g s o f l e n g t h 6 w h e r e \\ c h a r a t e r s a r e l e t t e r s a r e n e m b e r s) - (# o f a l l p o s s i b l e \\ s t r i n g s o f l e n g t h 6 w h e r e c h a r a t e r s a r e o n l y l e t t e r s) \\ = {(36)}^{6} - {(26)}^{6} \\ = 1867866560 \\ p_{7} = (# o f a l l p o s s i p l e s t r i n g s o f l e n g t h 7 w h e r e \\ c h a r a t e r s a r e l e t t e r s a r e n e m b e r s) - (# o f a l l p o s s i b l e \\ s t r i n g s o f l e n g t h 7 w h e r e c h a r a t e r s a r e o n l y l e t t e r s) \\ = {(36)}^{7} - {(26)}^{7} \\ = 70332353920 \\ p_{8} = (# o f a l l p o s s i p l e s t r i n g s o f l e n g t h 8 w h e r e c h a r a t e r s \\ a r e l e t t e r s a r e n e m b e r s) - (# o f a l l p o s s i b l e \\ s t r i n g s o f l e n g t h 8 w h e r e c h a r a t e r s a r e o n l y l e t t e r s) \\ = {(36)}^{8} - {(26)}^{8} \\ = 26122842880 \\ \Rightarrow p_{6} + p_{7} + p_{8} \\ \Rightarrow 2684483063360 \\ T h e f o l l o w i n g i s w r o n g a n s w e r \dots \\ 6 (10) {(36)}^{5} \\ W e h a v e d o u b l e c o u n t i n g . \end{array}