How many numbers can we form using 0,1,2,3,4,5,6,7,8,9 only once below

Question

How many numbers can we form using 0,1,2,3,4,5,6,7,8,9 only once below 1000 and is divided by 5?

A) 154
B) 155
C) 156
D) 157
E) 158

chetan2u · Accepted Answer

If the number is, say, ABC..
If the question means we are looking for 3-digit codes
I) First restriction....
 C can be only 0 or 5, as the number is divisible by 5--- 2 ways 
2) Second restriction....
 It has to be less than 1000, so A and B can be any out of remaining 9 and then 8, so 9*8 ways

Total 9*8*2=144

Other way would be ..
When question asks for integers irrespective of digits, then
 1) 3-digit number..... 
When C is 0---ABC can be 9*8*1=72
When C is 5 ---ABC can be 8*8*1=64, as A cannot be 0
 2) 2-digit number... 
When C is 0, BC can be 9*1
When C is 5, BC can be 8*1
 3) single digit number 
0 and 5, hence 2

Total 72+64+17+2=155

satya2029 · Answer

CASE 1 
Three digit numbers that end with "0"
 For First digit we have 9 options, For second 8, So total=72
Three digit numbers that end with "5"
For first digit we have 8 options, For second again 8, So total=64
 CASE 2.  
Two digit numbers that end with "0"
9 Options
Two digit numbers that end with "5"
8 options
So total=17
 CASE 3. 
  0 and 5  are also in the list
TOTAL=72+64+17+2=155
B:)

hudacse6 · Answer

in case 3, we can,t take "0" as a first digit. Check it out.
 satya2029

satya2029 · Answer

@ 
Here CASE 3 for single digit number
0 and 5 are divisible by 5.
??

chetan2u · Answer

You are correct..
If we are looking for numbers and not 3-digit codes, 0 will also fit in

hudacse6 · Answer

for single digit number we have only one possiblities. like 0 0 5

chetan2u · Answer

Hi,
Why not 000 or 0..
You are looking for numbers and 0 is also a number..
Had it been POSITIVE numbers, 0 would not have been included..

hudacse6 · Answer

How many numbers can we form using 0,1,2,3,4,5,6,7,8,9 only once below 1000 and is divided by 5?

A) 154
B) 155
C) 156
D) 157
E) 158

If the number is, say, ABC..
If the question means we are looking for 3-digit codes
I) First restriction....
 C can be only 0 or 5, as the number is divisible by 5--- 2 ways 
2) Second restriction....
 It has to be less than 1000, so A and B can be any out of remaining 9 and then 8, so 9*8 ways

Total 9*8*2=144

Other way would be ..
When question asks for integers irrespective of digits, then
 1) 3-digit number..... 
When C is 0---ABC can be 9*8*1=72
When C is 5 ---ABC can be 8*8*1=64, as A cannot be 0
 2) 2-digit number... 
When C is 0, BC can be 9*1
When C is 5, BC can be 8*1
 3) single digit number 
0 and 5, hence 2

Total 72+64+17+2=155 
 
for single digit number we have only one possiblities. like 0 0 5

Hi,
Why not 000 or 0..
You are looking for numbers and 0 is also a number..
Had it been POSITIVE numbers, 0 would not have been included..

as the official answer is 154 so we could not divide 0 by 5 if we do it the answer goes to 155 which is not the official answer.

chetan2u · Answer

for single digit number we have only one possiblities. like 0 0 5

Hi,
Why not 000 or 0..
You are looking for numbers and 0 is also a number..
Had it been POSITIVE numbers, 0 would not have been included..

as the official answer is 154 so we could not divide 0 by 5 if we do it the answer goes to 155 which is not the official answer.

In that case OA is wrong. What is the source and OA will be B, if it is given numbers and NOT positive numbers.

hudacse6 · Answer

Hi,
Why not 000 or 0..
You are looking for numbers and 0 is also a number..
Had it been POSITIVE numbers, 0 would not have been included..

as the official answer is 154 so we could not divide 0 by 5 if we do it the answer goes to 155 which is not the official answer.

In that case OA is wrong. What is the source and OA will be B, if it is given numbers and NOT positive numbers.

It,s from Bangladeshi high standard NTCB book which is used all over the country for class XII.

hudacse6 · Answer

pushpitkc 
what's ur opinion about this one?

chetan2u · Answer

Then the book is wrong in its answer. 
If the logic of not taking 0 is divisiblity by numbers other than 5, most of the numbers will not fit in. 
Only 5,25,125 and 625 will fit in.

Only if it was POSITIVE numbers, then the answer would be 154

Posted from my mobile device

hudacse6 · Answer

@
chetan2u"]

Then the book is wrong in its answer. 
If the logic of not taking 0 is divisiblity by numbers other than 5, most of the numbers will not fit in. 
Only 5,25,125 and 625 will fit in.

Only if it was POSITIVE numbers, then the answer would be 154

Posted from my mobile device

I also think they take Only postive numbers here. as 0 neither positive nor negative. so answer 154.

Kinshook · Answer

Form xy0 
9*8 = 72

Form xy5
8*8 = 64

Form x0
9

Form x5
8

Form 0

Form 5

72 + 64 + 9 + 8 + 1 + 1 = 155

IMO B

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How many numbers can we form using 0,1,2,3,4,5,6,7,8,9 only once below

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