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Question Number 120028 by Don08q last updated on 28/Oct/20

	Answered by bramlexs22 last updated on 29/Oct/20
	$(a) say three particular women is { (w_1 ),(w_2 ),(w_3 ) :} ■=woman particular □= the other person □■□■□■□■□⇒C _3^5 ×C _3^4 ×3!×5! = 10×3×6×120 =180×120=21,600$
	$(a) s a y t h r e e p a r t i c u l a r w o m e n i s {\begin{cases} w_{1} \\ w_{2} \\ w_{3} \end{cases}$ $◼ = w o m a n p a r t i c u l a r$ $◻ = t h e o t h e r p e r s o n$ $◻ ◼ ◻ ◼ ◻ ◼ ◻ ◼ ◻ \Rightarrow C_{3}^{5} \times C_{3}^{4} \times 3! \times 5!$ $= 10 \times 3 \times 6 \times 120$ $= 180 \times 120 = 21, 600$
	Answered by mr W last updated on 29/Oct/20

	$(a)$ $◻ M ◻ M ◻ M ◻ W ◻ W ◻$ $◻ = p l a c e f o r t h r e e p a r t i c u l a r w e m e n$ $C_{3}^{6} \times 3! \times 5! = 14 400$ $(b)$ $◻ M ◼ M ◼ M ◻$ ${(1 + x + x^{2} + . . .)}^{2} {(x + x + x^{3} + . . .)}^{2}$ $= \frac{x^{2}}{{(1 - x)}^{4}} = x^{2} \underset{k = 0}{\sum^{\infty}} C_{3}^{k + 3} x^{k}$ $k = 3, C_{3}^{6}$ $\Rightarrow C_{3}^{6} \times 3! \times 5! = 14 400$ $(c)$ $\frac{(8 - 1)!}{2} = \frac{7!}{2} = 2520$
	Commented by bramlexs22 last updated on 29/Oct/20

	$(a) h o w d o y o u c h o i c e 3 w o m a n p a r t i c u l a r$ $f r o m 5 w o m a n ?$
	Commented by mr W last updated on 29/Oct/20

	$t h e y a r e t h r e e p a r t i c u l a r w o w e n .$ $w e s h o u l d n o t c h o o s e t h e m .$
	Commented by bramlexs22 last updated on 29/Oct/20

	$o o i t d o e s m e a n t t h e t h r e e w o m a n$ $p a r t i c u l a r f i x ?$
	Commented by mr W last updated on 29/Oct/20

	$y e s . {l e t}^{'} s s a y t h e w e m e n a r e A, B, C, D, E .$ $t h e t h r e e p a r t i c u l a r w e m e n a r e$ $A, B, C . t h e y a r e f i x e d .$
	Commented by Don08q last updated on 29/Oct/20

	$Thank you Sir, b u t w h y^{6} C_{3} a n d n o t^{6} P_{3}$
	Commented by mr W last updated on 29/Oct/20

	$C_{3}^{6} \times 3! = P_{3}^{6}$
	Commented by Don08q last updated on 29/Oct/20

	$OK . Thank you$
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