Answer:
There are 360 such numbers.
Step-by-step explanation:
The number of 6-digit numbers, formed using each digit from 1 to 6 excactly once, means we can have numbers like
123456, 123465, 123546,123564,.... 654321
The number of such numbers is given by 6! because we have a choice of 6 numbers for the first digit, 5 left for the next, ... until the last digit has only one choice.
6! = 6*5*4*3*2*1 = 720
We know that 1+2+3+4+5+6 = 21 is divisible by three, so all 720 numbers are divisible by 3.
However, to be divisible by six, we need a number divisible by three AND divisible by two.
Thus, out of the 720 numbers, we need count only the even numbers, which are exact half of the 720, or 360.
Therefore there are 360 6-digit numbers, formed using each digit from 1 to 6 exactly once, are divisible by 6.
