# 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 Option 1) 312 Option 2) 3125 Option 3) 120 Option 4) 216

As we learnt in

Number of Permutations without repetition -

Arrange n objects taken r at a time equivalent to filling r places from n things.

- wherein

Where

We have 2 cases.

Case I: 0, 1, 2, 3, 6

Case II: 1, 3, 4, 6, 7

Total number of such numbers = 216

Correct option is 4.

Option 1)

312

This is an incorrect option.

Option 2)

3125

This is an incorrect option.

Option 3)

120

This is an incorrect option.

Option 4)

216

This is the correct option.

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