Five digit number divisible by $3$ is formed using $0,1,2,3,4,6$ and $7$ without repetition. Total number of such numbers are?:
$(1)312$
$(2)3125$
$(3)120$
$(4)216$
My answer is coming out to be $504$. I don't know where I am going wrong.
Please help
Best Answer
First thing 5 digit number can't be start with zero.
Make groups of numbers so that sum of these numbers are divisible by 3.
{7,0,3,6,2},{6,4,7,1,0},{6,4,2,3,0},{0,1,2,3,6},{7,6,1,3,4}
5-digit numbers containing 0 $= 4(4 \times 4 \times 3 \times 2 \times 1) = 384$
5-digit numbers not containing 0 $= 5 \times 4 \times 3 \times 2 \times 1 = 120$
If we add these two cases we have 504 numbers.
So above answers (1),(3),(4) are wrong.
Total 5-digit numbers that we can made from above digits are $= 6 \times 6 \times 5 \times 4 \times 3 = 2160$
So I think something wrong in given options.