Question

find the number of numbers less than 1000 and divisible by 5 which can be formed with the digits 0 1 2 3 4 5 6 7 8 9 without repetition

Answer 1

@imqwerty

Answer 2

@imqwerty fast :P

Answer 3

you are taking too long such a small sum:)

Answer 4

a number divisible by 5 has either 5 at end or 0 at end
so total such number will include all numbers of 1 digit , 2 digits...

1 digit nos are easy to count they are-5

2 digits nos -
we consider 2 cases one with 0 at the end and one with 5 at the end A
A] 0 at the end
1st place can be filled with-1,2,3,4,5,6,7,8,9 and 0 is fixed at 2nd place
so total numbers=9x1=9

B]5 at end
1st place can be filled with-1,2,3,4,6,7,8,9=8nos
we didn't take 0 cause then it wuld be a single digit no we also didn't take 5 cause its already set at 2nd place
so total nos=8x1=8

total 2 digit nos=17

3 digit nos-
A] 0 at end
1st place can be filled with-1,2,3,4,5,6,7,8,9=9nos
2nd place can be filled with 8 nos cause 1 number will be consumed in this^ step=8nos left to fill 2nd place
3rd place has 0=1no
so total combinations =9x8

B] 5 at end
1st place can be filled with-1,2,3,4,6,7,8,9=8nos
2nd place can be filled with 8 nos cause we can take 0 here along with the 7 digits left after filling 1st place=8nos
3rd place has 5 =1no
total nos=8x8

total 3 digit nos=72+64=136

total nos=136+17+9
=162

Answer 5

wrong answer is 154

Answer 6

i wrote in brief :D

Answer 7

lol wait

Answer 8

hey i did that correct i jst made calculation mistake :P
its 72+64+17+1=154

Answer 9

i wrote that 9 by mistake :)P
total i digit nos=1
total 2 digit nos=17
total 3 digit nos=72+64
total=154
>.<

Answer 10

*1 digit nos

Answer 11

how did you get the 3 digit numbers pls explain

Answer 12

the three digit numbers are obtained taking into account two cases

Answer 13

yeah 0 and 5

Answer 14

i got the 0 part just explain me the the 5 part

Answer 15

first 0: the first digit can be filled with 9 choices.. second will be 8 and since 0 is fixed so we get 9*8 = 72 numbers ending in 0 with three digits

Answer 16

yeah even i got that

Answer 17

see 5 is fixed.. so first digit can be filled in 8 ways..since 0 can not come in first place so second has 8 options..every number except for 5: so we have 8*8 = 64