Question

Using all or some of the digits 2, 3, 4 and 5, numbers greater than 500 without repeating digits. How many numbers does he write?

Answer 1

There are 30 numbers greater than 500, using 5, 4, 3, 2 with no repeats

Explanation:

For a three-digit number the number must begin with 5. There are 3 choices for the remaining two places, so six possibilities.

523

524

532

534

542

543

For a four-digit number, any of the 2, 3, 4, 5 can be in the thousands places (four choices) then three choices for the hundreds place, then two choices for the tens place, then one choice for the one place:

4•3•2•1

This is 4!

There are 24 possibilities for the four-digit number.

2345 4235

2354 4253

2435 4325

2453 4352

2534 4523

2543 4532

3245 5234

3254 5243

3425 5324

3452 5342

3524 5423

3542 5432

In total there are 30 numbers.