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Rogue Trooper Redux Free Download. Alex Brenner. there are many cracks.Dear Brothers and Sisters.Q:

Counting combinations

Find the number of two digit numbers that can be formed using the digits 1,2,3,4 and 5 and that can be exactly written using the digits 3,4,5.
This is what I tried.

First factor of the result is simply the number of such numbers that can be formed using the digits $1,2,3$ or $4,5$. These can be calculated by counting the ways of arranging these digits.
$$1 \times 2 = 2,1 \times 3 = 3,1 \times 4 = 4,1 \times 5 = 5,2 \times 3 = 6,2 \times 4 = 8,2 \times 5 = 10 \qquad \text{such that} \qquad 1 + 2 + 3 + 4 + 5 = 8 + 10 = 18$$
We still have to subtract the number of such numbers that can’t be written exactly by the given digits.
$$ 2 \times 2 = 4, 1 \times 3 = 3, 1 \times 4 = 4, 1 \times 5 = 5 \qquad \text{such that} \qquad 3 + 4 + 5 = 8 \qquad \text{such that} \qquad 3 = 8 – 3 = 5$$
We have to consider a particular digit, for example $3$. Then the number of ways to write it in exactly by $3$, $4$, $5$, $4$, $5$ and $3$, $4$, $5$, $4$, $5$ are respectively $2,2,1,1,1$ and so we have to multiply these by two.
$$(2) \times (2) \times (1) \times (1) \times (1) = 8 \times 4 \times 2 \times 1 = 32$$
And the final result is $18 – 32 = 46$
Is my method correct and is there any other approach?

A:

Your approach is correct but I would do it differently.
$1\times1, 1\times2, 1\times3, 1\times4, 1\times5$ are solutions to $1+2+3+4+5=8$. There are $12$ of them.
$1\times2, 1\times

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