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Question Number 123771 by benjo_mathlover last updated on 28/Nov/20

Commented by benjo_mathlover last updated on 28/Nov/20

$l e t ⧫ = m a n, ♡ = w o m a n$ $⧫ ♡ ⧫ ♡ ⧫ ♡ ⧫ ♡ ⧫ ♡ ⧫ ♡ ⧫ =$ $3! \times C_{3}^{6} \times 5! \times 42$ $p (A) = \frac{3! \times C_{3}^{6} \times 7!}{10!} = \frac{6 \times 20 \times 7!}{10 \times 9 \times 8 \times 7!} = \frac{1}{6}$
Commented by benjo_mathlover last updated on 28/Nov/20

$i t i s c o r r e c t ?$
Commented by mr W last updated on 28/Nov/20

$c o r r e c t! b u t w h a t d i d y o u t h i n k b y$ $w r i t i n g 5! \times 42 ?$ $t o p l a c e t h r e e w o m e n i n t o t h e s i x$ $p l a c e s b e t w e e n t h e 7 m e n t h e r e a r e$ $C_{3}^{6} w a y s, t o a r r a n g e t h e 3 w o m e n a n d$ $7 m e n t h e r e a r e 3! \times 7! w a y s,$ $t h e r e f o r e t h e a n s w e r i s$ $p (A) = \frac{C_{3}^{6} \times 3! \times 7!}{10!}$
Commented by benjo_mathlover last updated on 28/Nov/20
because at both ends have to be occupied by men then many ways 6x7 = 42 sir
Commented by mr W last updated on 28/Nov/20

$b u t w e {d o n}^{'} t n e e d t o a r r a n g e t h e t w o$ $m e n a t e n d s a t f i r s t a n d t h e n t h e$ $o t h e r f i v e m e n, w e c a n a r r a n g e a l l$ $7 m e n a l l a t o n c e . c e r t a i n l y t h e$ $r e s u l t i s t h e s a m e :$ $7 \times 6 \times 5! = 7!$
Commented by benjo_mathlover last updated on 28/Nov/20

$o o t h a n k y o u s i r$
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