Find the sum of all numbers greater than $10000$ formed by using all digits $0,1,2,4,5$

Hint: imagine writing all of them up, one below the other, as though you're about to add them up the way you (probably) learned in elementary school. How many have a 1 in the first column? A 2? A 3? What does that column sum to? Do this for each column, then put together the results.


HINT:

You are correct that there are $96=4!\cdot4$ numbers as they can't start with $0$.

Now write down all the combinations and add them.

As an example, for $1$, we have $$\begin{align}\color{red}{10245\\10254\\10425\\10452\\10524\\10542}\\\color{blue}{12045\\12054\\12405\\12450\\12504\\12540}\\\color{green}{14025\\14052\\14205\\14250\\14502\\14520}\\\color{purple}{15024\\15042\\15204\\15240\\15402\\\hspace{-0.5cm}\color{black}+15420}\\\hline313326\end{align}$$

Tags:

Combinatorics

Algebra Precalculus

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