How many numbers greater than $6000$ and less than $7000$ can be formed using the digit $0, 1, 2, - - -, 9$ which are divisible by $5$ and the digit can be repeated?

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Solution

-Unit's place only $0, 5$ can be placed - $2$ ways.

Ten's place all number can be placed - $10$ ways.

Hundred's place all number can be placed - $10$ ways.

Thousand's place only 6 can be placed - $1$ way.

total ways $= 2 \times 10 \times 10 = 200.$

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How many numbers greater than 6000 and less than 7000 can be formed using the digit 0,1,2,−−−,9 which are divisible by 5 and the digit can be repeated?

-Unit's place only 0,5 can be placed - 2 ways.Ten's place all number can be placed - 10 ways.Hundred's place all number can be placed - 10 ways.Thousand's place only 6 can be placed - 1 way.total ways =2×10×10=200.

How many numbers greater than $6000$ and less than $7000$ can be formed using the digit $0, 1, 2, - - -, 9$ which are divisible by $5$ and the digit can be repeated?

-Unit's place only $0, 5$ can be placed - $2$ ways.

Ten's place all number can be placed - $10$ ways.

Hundred's place all number can be placed - $10$ ways.

Thousand's place only 6 can be placed - $1$ way.

total ways $= 2 \times 10 \times 10 = 200.$