How many permutations of the letters of the word EINSTEIN are possible if the EIN groups must not be next to eachother?


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Question Number 166787 by nadovic last updated on 27/Feb/22

$How many permutations of the$ $letters of the word EINSTEIN are$ $possible if the EIN groups must not$ $be next to eachother ?$
Commented by mr W last updated on 28/Feb/22

$d o y o u m e a n ‘ ‘ t h e r e m u s t b e t w o$ $E I N g r o u p s, b u t t h e y m u s t n o t b e$ $n e x t t o e a c h {o t h e r}^{″} ? t h e n t h e r e a r e$ $o n l y f o l l o w i n g 6 p o s s i b i l i t i e s :$ $E I N S T E I N$ $E I N T S E I N$ $S E I N T E I N$ $T E I N S E I N$ $E I N S E I N T$ $E I N T E I N S$
Commented by nadovic last updated on 28/Feb/22

$I think you did not include the$ $different ways in which the letters$ $in the EIN groups can also be$ $arranged differently within$ $themselves . L i k e E N I S T N I E,$ $w i t h o u t s t i l l b r i n g i n g t h e g r o u p s$ $n e x t t o e a c h o t h e r . That will give$ $more than 6 ways .$
Commented by mr W last updated on 28/Feb/22

$y o u {d i d n}^{'} t m a k e i t c l e a r i n t h e$ $q u e s t i o n w h a t y o u e x a c t l y m e a n w i t h$ $‘ ‘ E I N {g r o u p s}^{″}!$ $w h e n t h e q u e s t i o n m e a n t t h a t w h a t$ $y o u j u s t s a i d, t h e n t h e a n s w e r i s$ $6 \times {(3!)}^{2} = 216 .$
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