Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly three aces in each combination.
$3$ aces can be selected from $4$ aces in ${^{4}}{C}_{3} = \dfrac{4!}{1! \times 3!} = 4$ ways
The remaining $2$ cards can be selected from the remaining $52 - 4 = 48$ cards in
${^{48}}{C}_{2} = \dfrac{48!}{46! \times 2!} = \dfrac{48 \times 47}{2} = 1128$ ways
$\therefore \;$ Number of $5$ card combinations that can be made from a deck of $52$ cards so that there are exactly $3$ aces in each combination $= 4 \times 1128 = 4512$ combinations