Digits & Decimals - Chapter 1 Question 2

[Guest]

what is the sum of all the possible 3-digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can be used only one in each number?

The answer explains the following:

6 ways to arrange the 3 digits:
1) 345
2) 354
3) 435
4) 453
5) 534
6) 543

Notice that each digit appears twice in the hundreds column, twice in the tens column, and twice in the units column.
Therefore you can use your knowledge of place value to find the sum quickly:
100(24) + 10(24) + 1(24) = 2400 + 240 + 24 = 2664

Probably very simple ... but I am struggling to understand where the (24) comes from ?

Thanks in advance.

[StaceyKoprince]

No problem! This could have been laid out a bit more clearly.

Place value says that you can add up the values of the digits and multiply by their place value (units, tens, hundreds, etc)

We have three digits: 3, 4, and 5
each digit shows up twice in the hundreds place. So that's 3+3+4+4+5+5 = 24. Multiply by the place (100) to get 2400
each digit shows up twice in the tens place. Add them up (24 again) and multiply by the place (10 this time) to get 240
and the same thing for the units place: 24*1 = 24.

Then add those three numbers up. Make sense?

[Guest]

Got it. Thanks Stacey.

[brian]

Glad that Stacey was able to help out.
-Brian Lange