Question-95723

Question Number 95723 by i jagooll last updated on 27/May/20

Commented by bobhans last updated on 27/May/20

the case is ssma with there are 5 women 2 men sitting in 7 chairs with no 2 men sitting side by side

Answered by Rio Michael last updated on 27/May/20

the 5 girls can stand in a row in 5! ways

let the girls be labeled as below

G_{1} G_{2} G_{3} G_{4} G_{5}

the first boy coming in has 6 vacancies

the second has 5 vacanciies

the third has 4 vacancies so

\Rightarrow number of ways = 5! \times 6 \times 5 \times 4 = 14 400 ways

Commented by mr W last updated on 27/May/20

14400 i s c o r r e c t! R i o M i c h a e l s i r :

w h e r e d o y o u t h i n k y o u a r e w r o n g ?

Commented by i jagooll last updated on 27/May/20

your answer not include G G BGBGGB ?

Commented by Rio Michael last updated on 28/May/20

well sir i was in a hurry on that problem

when the others dropped thier solution

i thought i misread it .

Answered by bobhans last updated on 27/May/20

totally arrangement = 8!

2 boy stand are together = C_{2}^{3} . 3! 6!

then = 8! - 6.6! = 6! \times 50

Answered by mr W last updated on 27/May/20

M E T H O D I

b e t w e e n t w o b o y s t h e r e m u s t b e a t l e a s t

o n e g i r l .

w e a r r a n g e a t f i r s t t h e 5 g i r l s, t h e r e

a r e 5! w a y s .

G G G G G

t h e 3 b o y s c a n n o w t a k e t h r e e o f

6 p o s i t i o n s () . t h e r e a r e C_{3}^{6} \times 3! w a y s .

s o t o t a l l y t h e r e a r e C_{3}^{6} \times 3! \times 5! = 14400

w a y s .

M E T H O D I I

t o a r r a n g e 8 c h i l d r e n t h e r e a r e 8!

w a y s .

t o a r r a n g e t h e m s u c h t h a t t h r e e b o y s

a r e t o g e t h e r, t h e r e a r e 6! \times 3! w a y s .

t o a r r a n g e t h e m s u c h t h a t t w o a n d

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

t h e r e a r e C_{2}^{3} \times (7! - 2 \times 6!) \times 2! w a y s .

t o t a l v a l i d a r r a n g e m e n t s :

8! - C_{2}^{3} \times (7! - 2 \times 6!) \times 2! - 6! \times 3! = 14400

Commented by john santu last updated on 28/May/20

oo yes \dots your right . i^{'} m using method II

but forgot something . ok thanks you

Commented by bobhans last updated on 28/May/20

how with GG G GG

with GGG G G ?

your answer included it ?

Commented by mr W last updated on 28/May/20

y e s, i n c l u d e d .

t h e b o y s c a n t a k e a n y t h r e e p o s i t i o n s

f r o m t h e 6 i n :

G G G G G

e x a m p l e s :

G G G G G

G G G G G

Commented by i jagooll last updated on 28/May/20

thank you sir