A whatsapp group contains 7 women and 3 men.If they are leaving the group one at a time from the group what is the probability of a woman leaving then a man leaving and so on alternately until only a woman is remaining?


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Question Number 55344 by Necxx last updated on 21/Feb/19

$A w h a t s a p p g r o u p c o n t a i n s 7 w o m e n$ $a n d 3 m e n . I f t h e y a r e l e a v i n g$ $t h e g r o u p o n e a t a t i m e f r o m t h e$ $g r o u p w h a t i s t h e p r o b a b i l i t y o f a$ $w o m a n l e a v i n g t h e n a m a n l e a v i n g$ $a n d s o o n a l t e r n a t e l y u n t i l o n l y a$ $w o m a n i s r e m a i n i n g ?$
Commented by mr W last updated on 22/Feb/19

$W M W M W M W W W W \to l e a v i n g$ $\frac{7 \times 3 \times 6 \times 2 \times 5 \times 1 \times 4!}{10!}$ $= \frac{3 \times 2}{10 \times 9 \times 8}$ $= \frac{1}{120}$
Commented by necx1 last updated on 23/Feb/19

$y e a h . . . . T h a n k s$
Commented by rahul 19 last updated on 23/Feb/19

$S i r, p l e x p l a i n m o r e w h a t y o u h a v e d o n e .$
Commented by mr W last updated on 24/Feb/19

$t o t a l n u m b e r o f w a y s t o a r r a n g e 10$ $p e r s o n s i s 10! .$ $s u c h t h a t t h e p e r s o n s l e a v e w h a t s a p p$ $i n t h e w a y a s r e q u e s t e d i n t h e q u e s t i o n,$ $t h e p e r s o n s s h o u l d b e a r r a n g e d l i k e$ $t h i s :$ $W M W M W M W W W W \to l e a v i n g w h a t s a p p$ $w i t h W = w o m a n, M = m a n$ $t h e r e a r e 7! 3! s u c h a r r a n g e m e n t s,$ $t h e r e f o r e t h e p r o b a b i l i t y i s$ $\frac{7! 3!}{10!} = \frac{3!}{10 \times 9 \times 8} = \frac{1}{120}$
Commented by rahul 19 last updated on 25/Feb/19

$t h a n k U s i r!$
Commented by rahul 19 last updated on 25/Feb/19
Today is 25th Feb'19 ... why my comment shows 24th Feb'19 ? some technical error ...
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