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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

Arnaldo
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Shammy
  • 63

1 Answers1

1

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.

Amar
  • 847