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

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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