How-many-numbers-less-than-1000-and-divisible-by-5-can-be-formed-with-the-digits-0-1-2-3-4-5-6-7-8-9-each-digit-not-occuring-more-than-once-in-each-number-

Question Number 26473 by NECx last updated on 25/Dec/17

H o w m a n y n u m b e r s l e s s t h a n

1000 a n d d i v i s i b l e b y 5 c a n b e

f o r m e d w i t h t h e d i g i t s 0, 1, 2, 3, 4, 5

6, 7, 8, 9, e a c h d i g i t n o t o c c u r i n g

m o r e t h a n o n c e i n e a c h n u m b e r ?

Answered by mrW1 last updated on 26/Dec/17

o n e d i g i t n u m b e r s :

N_{1} = 1 (o n l y 5, w i t h o u t t h e n u m b e r 0)

t w o d i g i t s n u m b e r s :

t y p e X 0 : \Rightarrow 9

t y p e X 5 : \Rightarrow 8

\Rightarrow N_{2} = 9 + 8 = 17

t h r e e d i g i t s n u m b e r s :

t y p e X X 0 : \Rightarrow 9 \times 8 = 72

t y p e X X 5 : \Rightarrow 8 \times 8 = 64

\Rightarrow N_{3} = 72 + 64 = 136

\Rightarrow N = 1 + 17 + 136 = 154

Commented by NECx last updated on 26/Dec/17

o k s i r

Commented by NECx last updated on 26/Dec/17

t h a n k s s o m u c h s i r \dots .

I g o t 164 b u t t h e b o o k g o t 155

Commented by mrW1 last updated on 26/Dec/17

I h a v e e x c l u d e d t h e n u m b e r z e r o . I f z e r o

i s a l s o t a k e n i n t o a c c o u n t t h e n t h e

r e s u l t i s 155 .

Facebook Tweet Pin