How many different three-digit numbers can be formed w/ 2, 4, 6 used as many times as you like?

[ilovegod7]

How many different three-digit numbers can be formed using the digits 2, 4 and 6 if each digit can be used:

a). as many times as you would like

 

[stapel]

How many different three-digit numbers can be formed using the digits 2, 4 and 6 if each digit can be used:

a). as many times as you would like

Please re-read the "Read Before Posting" message, and then reply with a clear listing of your thoughts and efforts so far. Thank you!

Eliz.

 

[NotJeffM]

How many different three-digit numbers can be formed using the digits 2, 4 and 6 if each digit can be used:

a). as many times as you would like

We do not give answers. We help you solve the problem on your own. After all, when you take the test, we shall not be there to give you the answer.

I am going to give you a hint. This problem looks hard but becomes considerably easier if you break it down into parts.

How many distinct three-digit numbers can be formed using one of the digits 2, 4, and 6 three times?

If you learned some counting formulas, which formula applies to the question above? (You do not need a counting formula for this easy a problem, but it is good to see that the formula gives the same answer as common sense.)

How many distinct three-digit numbers can be formed using 4 twice and 2 once?

So, how many distinct three-digit numbers can be formed using one of the digits 2, 4, and 6 twice and either of the other two digits once?

This idea of breaking a problem into several easier problems is useful in many parts of mathematics.

 

[Steven G]

Try listing the numbers
222
224
242
422
226
262
622
244
424
442
266
626
662
....