sudhir3127 wrote:how many 4 digit number that are divisble by 4 can be formed using digits 0 to 7 if no digit is to occur more than once in each number.
a. 570
b. 370
c. 345
d. 440
OA is B
Firstly I must say its a really good question.
The property of any number to be divisible by 4 is its last 2 digits should be divisible by 4.
There are 3 such numbers, if 0 is placed in units place the number is divisible by 4
20
40
60
Therefore, 6*5*3 = 90 (6*5*3 because we are left with only 6 digits since 0 and 2 or 4 or 6 are already taken)
There is 1 such number where 0 can be at the tens place and the number is divisible by 4
04
Therefore, 6*5*1 = 30
Now the largest number that we can have from 0-7 is 77, therefore, from 0-77 there are 19 numbers which are divisible by 4
We have to subtract the above numbers because we have already taken them into account 19-4= 15
we also have to subtract 44 since digits cannot be repeated
we also have o subtract 08, 28, 48, 68 since we dont want any digit which is beyond 7
15-5 = 10
therefore, 5*5*10 = 250 (5*5*10 because we dont want 0 at the thousands place)
250+90+30 = 370
I think there is a better way of doing this question.
