Question

How many 6-digit even numbers between 640,000 and 645,000 can be formed using the digits given below? Use each digit only once.
4, 7, 0, 2, 6, 9

Answer 1

The first two digits must be 6 and 4.

The third digit must be between 0 (inclusive) and 5 (exclusive), so there are 2 choices for it (0 or 2).

The remaining three digits have no additional restrictions. There are 3! = 6 ways to permute them.

Then there are 2•6 = 12 such numbers.

640 279

640 297

640 729

640 792

640 927

640 972

642 079

642 097

642 709

642 790

642 907

642 970