Question

Write all possible three - digit numbers using the digit 6, 0, 4, when repetition digits is not allowed.

Answer 1

Hint: Since they ask to find the three digit number. Thus we have the place values hundreds, tens and units. Always remember that if we have zero we have to be careful. We do not keep zero in the place value of thousands. It would become a two digit number. So we need to put the zero in hundreds and units place only.

Complete step-by-step answer:
Given, digits 6, 0, 4.
Let’s see the possible arrangement of the digits,
$\Rightarrow$ 604, no digits are repeated.
$\Rightarrow$ 406, no digits are repeated.
$\Rightarrow$ 640, no digits are repeated.
$\Rightarrow$ 460, no digits are repeated.
$\Rightarrow$ 400, 406, 460, 466, 444, 404, 440, 446, 464, 600, 644, 666, 606, 660, 664, 646. As we can see in this two or three digits are repeated. So we don’t take this into count.
Hence, there are four possible three digit numbers that can be formed using the digits 6, 0, 4, without repetition of digit. The 3-digit numbers are 604, 406, 640 and 460.
So, the correct answer is “604, 406, 640 and 460”.

Note: In the question if they ask repetition of digit allowed write down the all numbers that are written above. The most important part here is the placing of the zero digit. Follow the procedure which is done above for any digit number for placing the zero digit. In the above question the largest three digit number is 640. The smallest three digit number is 406.