Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits…

Question

Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is \_\_\_\_\_\_\_.

Answer: 30

Accepted Answer

The number lies between 1000 and 3000, so the first digit is 1 or 2.

For divisibility by 4, the last two digits must form a number divisible by 4, using digits from the remaining pool without repetition.

Working through both cases (first digit 1, first digit 2) and enumerating valid last-two-digit pairs divisible by 4 from the remaining 5 digits, with the middle two digits filled from the rest:

$$\text{Total} = 30$$

Solutions · 1