How many 6-digit integers greater than 400,000 can be formed such that each of the digits 2, 3, 4, 5, 6 and 7 is used once in each 6-digit integer?

The question asks for a 6-digit number greater than 400,000.

The numbers that we can be used for the hundred-thousands digit is either 4, 5, 6 or 7. We have 4 choices.

4x?x?x?x?x?

For the ten-thousand digit, we can fit them with any number. Meaning, if we use 4 for the hundred-thousand, we can use the other 5 digits - 2, 3, 5, 6, 7. This also applies if we choose another number, let's say 2. We can then choose from 3, 4, 5, 6, 7. Again 5 digits, meaning 5 choices.

4x5x?x?x?x?

Use the same strategy for filling in the rest of the numbers and your equation looks like so.

4x5x4x3x2x1=?