A general case: we have totally n letters, among them n_1 times A, n_2 times B, n_3 times C, n_4 times D etc. (n_1 ,n_2 ,n_3 ,n_(4,) ...≥2, n>n_1 +n_2 +n_3 +n_4 +....) how many different words can be formed using these n letters such that same letters are not next to each other. see also Q107451.


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Question Number 107844 by mr W last updated on 13/Aug/20

$A g e n e r a l c a s e :$ $w e h a v e t o t a l l y n l e t t e r s, a m o n g t h e m$ $n_{1} t i m e s A, n_{2} t i m e s B, n_{3} t i m e s C,$ $n_{4} t i m e s D e t c .$ $(n_{1}, n_{2}, n_{3}, n_{4,} . . . ⩾ 2, n > n_{1} + n_{2} + n_{3} + n_{4} + . . . .)$ $h o w m a n y d i f f e r e n t w o r d s c a n b e$ $f o r m e d u s i n g t h e s e n l e t t e r s s u c h t h a t$ $s a m e l e t t e r s a r e n o t n e x t t o e a c h$ $o t h e r .$ $s e e a l s o Q 107451 .$
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