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Question Number 199031 by cortano12 last updated on 27/Oct/23

	Answered by mr W last updated on 27/Oct/23

	$1)$ $C_{3}^{4} \times 3! \times C_{2}^{5} \times 2! = 4 \times 6 \times 10 \times 2 = 480$ $2)$ $\frac{4}{6} \times C_{4}^{6} \times 4! - C_{2}^{4} \times 2! = 228$ $3)$ $a l l : 9! = 362880$ $d i v i s i b l e b y 4 : 16 \times 7! = 80640$ $4)$ $6! \times 3! = 4320$
	Commented by cortano12 last updated on 27/Oct/23

	$explain sir why 16 \times 7!$
	Commented by mr W last updated on 27/Oct/23

	$a b c d e f g x y$ $s u c h t h a t t h i s n u m b e r i s d i v i s i b l e$ $b y 4, x y m u s t b e d i v i s i b l e b y 4 . t h e r e$ $a r e 16 p o s s i b l i t i e s f o r x y :$ $12 / 16 / 24 / 28 / 32 / 36 / 48 / 52 / 56 / 64 / 68 / 72 / 76 / 84 / 92 / 96$ $t o a r r a n g e t h e r e m a i n i n g 7 d i g i t s$ $a b c d e f g t h e r e a r e 7! w a y s . s o t o t a l l y$ $t h e r e a r e 16 \times 7! v a l i d n u m b e r s .$
	Commented by cortano12 last updated on 27/Oct/23

	$thank you sir$
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