

Name: Beth
Who are you: Parent (Middle)
How many different threedigit numbers can you make using the numbers 2, 5, 7, 8 using the digits any number of times?


Hi Beth,
I have two responses for you.
How many different onedigit numbers can you make using the numbers 2, 5, 7, 8 using the digits any number of times?
That's easy, there are four. They are 2, 5, 7 and 8.
How many ways can you extend these to twodigit numbers?
Each of the four onedigit numbers can be extended to a twodigit number by appending one of the onedigit numbers. Thus you get
22, 25, 27, 28
52, 55, 57, 58
72, 75, 77, 78 and
82, 85, 87,88
Thus each of the four onedigit numbers can be extended to a twodigit number in four ways. Thus there are
4 × 4 = 16 possible twodigit numbers.
How many ways can you extend these to threedigit numbers?
Penny
and
Hi Beth.
Pick a number: 2, 5, 7, or eight.
How many choices do you have? Four.
Now for each of those four, pick each number from the list 2, 5, 7, 8.
How many pairings do you have for each of the original choices? Four
again. That means 4 x 4 ordered pairs.
Repeat the process one more time. You have sixteen ordered pairs now.
For each pair, pick each of the four digits again. That makes 16 x 4
ordered triples.
An ordered triple is a three digit number, so we've solved our question.
Hope this helps,
Stephen La Rocque.



