Question

How many even 3 digit positive integers can be written using the numbers 3,4,5,6,and 7?

Answer 1

Answer

24 or 50 digits (look below)

Explanation

(If each digit can be used only once)

Even numbers end with an even number, the 2 numbers here are 4 and 6.

Let’s consider the numbers being {a,b,c,d,e}

D and E are the even numbers 4 and 6.

Now for the combination you can have

4 • 3 • e

as you can have 4 choices {a,b,c,d} then 3 choices {b,c,d}

This can also be applied for second even number

4 • 3 • d


This results in 24 digits

Explanation (if each digit can be used more than once)

5 • 5 • e and 5 • 5 • f

This results in 50 combinations

Answer 2

I got 45, but I may be wrong.

Explanation:

When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.

To answer this question, we just have to find as many possible combinations following the guidelines provided.

334

344

354

364

374

434

444

454

464

474

534

544

554

564

574

634

644

654

664

674

336

346

356

366

376

436

446

456

466

476

536

546

556

566

576

636

646

656

666

676

736

746

756

766

776