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Question Number 114797 by bemath last updated on 21/Sep/20

T h e r e a r e 6 p e o p l e g o i n g t o s i t i n

a c i r c l e . T h e n u m b e r o f a r r a n g e m e n t s

t h e y s i t i f t h e r e a r e 2 p e o p l e w h o

a l w a y s s i t n e x t t o e a c h o t h e r

Answered by mr W last updated on 21/Sep/20

2 \times 4! = 48

Commented by bemath last updated on 21/Sep/20

g a v e k u d o s

Commented by bemath last updated on 21/Sep/20

s i r w h y n o t C_{2}^{6} \times 2 \times 4! s i r

Commented by mr W last updated on 21/Sep/20

w e h a v e a l w a y s t w o p e o p l e n e x t t o

e a c h o t h e r . h e r e i t i s m e a n t t h a t t w o

p a r t i c u l a r p e o p l e a r e n e x t t o e a c h

o t h e r, s o y o u c a n n o t s e l e c t t w o a n y

p e o p l e f r o m 6 .

Commented by bemath last updated on 21/Sep/20

t h e c o n d i t i o n s u n d e r w h i c h t h e

C_{2}^{6} i s t a k e n i n t o a c c o u n t s i r

Commented by mr W last updated on 21/Sep/20

i f t h e q u e s t i o n i s :

t h e r e a r e 10 s e a t s o n a r o u n d t a b l e .

i n h o w m a n y w a y s c a n 6 p e o p l e s i t

o n t h e t a b l e s u c h t h a t a t l e a s t t w o

p e o p l e a r e n e x t t o e a c h o t h e r ?

Commented by bemath last updated on 21/Sep/20

f o r t h i s q u e s t i o n t h e a n s w e r i s

C_{2}^{6} \times 2 \times C_{6}^{10} \times 4! s i r

Commented by mr W last updated on 21/Sep/20

C_{2}^{6} \times 2 \times C_{4}^{8} \times 4!

o r

C_{2}^{6} \times 2 \times P_{4}^{8}

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