Question

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position? [

Answer 1

Answer:

Since the four digit number is divisible by 6,it has to be divisible by 2&3.

So the thousands place can have all numbers except 0.The hundreds place and tens place can have all the six numbers 0,1,2,3,4,5.But the units place can have only 0,2,4 - since only an even number can be divisible by 2.

So the total number of even numbers are=5×6×6×3 =540.

So every third number in this will be a multiple of 3=540×1/3=180.

So 180 numbers are multiples of 6.