Weighting a fixed sum

Let $X$ , $Y$ , $Z$ be independent and identically distributed random variables. Given that $X + Y + Z = 12$ , compute $E[2X + 3Y]$ .

Show hints (2)+

By symmetry each of $X,Y,Z$ has the same conditional mean given their sum - what is it?
Then apply linearity to the weighted combination $2X+3Y$ .

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