An 8 digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is? a)72(7i) b)18(7i) c)40(7i) d)36(7i) please I mean factorial by i.The part of my screen where the factorial symbol is isnt functioning.Thanks


Question and Answers Forum

All Questions Topic List
Permutation and Combination Questions
Previous in All Question Next in All Question
Previous in Permutation and Combination Next in Permutation and Combination
Question Number 52276 by Necxx last updated on 05/Jan/19

$A n 8 d i g i t n u m b e r d i v i s i b l e b y 9 i s$ $t o b e f o r m e d u s i n g d i g i t s f r o m$ $0 t o 9 w i t h o u t r e p e a t i n g t h e d i g i t s .$ $T h e n u m b e r o f w a y s i n w h i c h t h i s$ $c a n b e d o n e i s ?$ $a) 7 2 (7 i) b) 18 (7 i) c) 40 (7 i) d) 36 (7 i)$ $p l e a s e I m e a n f a c t o r i a l b y i . T h e$ $p a r t o f m y s c r e e n w h e r e t h e f a c t o r i a l$ $s y m b o l i s i s n t f u n c t i o n i n g . T h a n k s$
	Answered by mr W last updated on 06/Jan/19

	$w e h a v e 10 d i g i t s, b u t w e n e e d o n l y 8$ $f r o m t h e m t o f o r m a 8 - d i g i t n u m b e r .$ $t h a t i s t o s a y, w e m u s t t a k e 2 o f t h e$ $10 d i g i t s a w a y . b u t w h i c h d i g i t s s h a l l$ $w e t a k e a w a y ? i t i s r e q u e s t e d t h a t$ $t h e 8 - d i g i t n u m b e r s a r e d i v i s i b l e b y$ $9 . w e k n o w a n u m b e r i s d i v i s i b l e b y 9$ $o n l y w h e n t h e s u m o f i t s d i g i t s i s$ $d i v i s i b l e b y 9 . s i n c e 0 + 1 + 2 + . . . + 9 = 45,$ $i t m e a n s w h e n w e t a k e a l l 10 d i g i t s,$ $t h e n u m b e r s f o r m e d b y t h e m a r e a l w a y s$ $d i v i s i b l e b y 9, s i n c e 45 i s d i v i s i b l e b y 9 .$ $w h e n w e w a n t t o r e m o v e t w o d i g i t s t o$ $f o r m 8 - d i g i t n u m b e r s w h i c h r e m a i n$ $d i v i s i b l e b y 9, t h e s u m o f t h e s e t w o$ $d i g i t s m u s t b e d i v i s i b l e b y 9 . t h e r e a r e$ $o n l y f o l l o w i n g 5 p o s s i b i l i t i e s :$ $w e t a k e 0 a n d 9 a w a y,$ $w e t a k e 1 a n d 8 a w a y,$ $w e t a k e 2 a n d 7 a w a y,$ $w e t a k e 3 a n d 6 a w a y,$ $w e t a k e 4 a n d 5 a w a y .$ $w h e n w e t a k e 0 a n d 9 a w a y, w i t h t h e$ $r e m a i n i n g 8 d i g i t s 1 t o 8 w e c a n f o r m$ $t o t a l l y 8! n u m b e r s .$ $w h e n w e t a k e 1 a n d 8 a w a y, w i t h t h e$ $r e m a i n i n g 8 d i g i t s (o n e o f t h e m i s 0)$ $w e c a n f o r m t o t a l l y o n l y 7 \times 7! n u m b e r s$ $s i n c e 0 c a n n o t b e p l a c e d i n t h e f i r s t$ $p o s i t i o n .$ $s i n c e w e h a v e 4 s u c h s i m i l a r w a y s$ $t o t a k e t w o d i g i t s a w a y, w e c a n t o t a l l y$ $f o r m 4 \times 7 \times 7! n u m b e r s .$ $s o t h e r e s u l t i s 8! + 4 \times 7 \times 7! = 36 \times 7!$ $\Rightarrow a n s w e r d) i s c o r r e c t .$
	Commented by Necxx last updated on 06/Jan/19

	$w o w . . . . . T h a n k y o u s i r .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum