Probability of picking exactly one ace?

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Poker hand: 5 cards. Deck: 52 cards.
$$\begin{pmatrix} 52\\ 5 \end{pmatrix}$$

There is 4 aces, number of outcomes to pick one ace: $$4*\begin{pmatrix} 52\\ 1 \end{pmatrix}$$
And at last, number of outcomes to fill slots for other 4 cards. 49 because, we don't won't to pick 3 remaining aces. $$\begin{pmatrix} 49\\ 4 \end{pmatrix}$$

Result:
$$\frac{ 4* \begin{pmatrix} 52\\ 1 \end{pmatrix} * \begin{pmatrix} 49\\ 4 \end{pmatrix} }{ \begin{pmatrix} 52\\ 5 \end{pmatrix} }$$

Can somebody explain why this answer is not correct?