We need to find the number of numbers we can form greater
than 5000 and divisible by 3.
Now we see that 3+4+5+6 = 18
which is divisible by 3 so any number which has all the digits will be divisible by
3.
Therefore we can have any 5 digit number. The number of
these possible is 4*4*3*2*1 = 72
Now to find the number of
4 digit numbers that satisfy this condition. We see that the only sets which are
divisible by 3 are 4,5,6,3 and 5,4,3,0 and 5,4,6,0
The
first digit can only be 5 or 6.
Now the numbers starting
with 5 and divisible by 3 are: 5604, 5640 , 5460 , 5406, 5064, 5064, 5304, 5340, 5034,
5043, 5403, 5430, 5643, 5634, 5436, 5463, 5346, 5364. We have 18
numbers
The numbers starting with 6 and divisible by 3 are:
6540, 6504, 6450, 6405, 6045, 6054, 6345, 6354, 6435, 6453, 6534, 6543. we have 12
numbers.
Therefore the total number of numbers is 18+ 12
+72 = 102
The required result is
102.
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