How many different numbers?

Question

How many different six digit numbers can be formed using three 5's, two 4's, and one 6?

Answer 1

This is a permutation with repetitions.

 

₆P₆ = 6! / (3!)(2!)

₆P₆ = 720 / (6)(2)

 

What is that number?

Answer 2

See Mark M.'s answer.

 

Here are all of the 6-digit numbers:

 

445556 445565 445655 446555 454556 454565
454655 455456 455465 455546 455564 455645
455654 456455 456545 456554 464555 465455
465545 465554 544556 544565 544655 545456
545465 545546 545564 545645 545654 546455
546545 546554 554456 554465 554546 554564
554645 554654 555446 555464 555644 556445
556454 556544 564455 564545 564554 565445
565454 565544 644555 645455 645545 645554
654455 654545 654554 655445 655454 655544