Total of 1820 different kinds of banquets can be made.
Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial. Combos' components can be chosen in any hierarchy.
[tex]$C_{12}(16)=\left(\begin{array}{l}16 \\ 12\end{array}\right)=\frac{16 !}{12 !(16-12) !}=\frac{16 \cdot 15 \cdot 14\cdot13}{4\cdot3 \cdot 2 \cdot 1}=1820[/tex]
[tex]$n=5$ $k=12$\\$x=\left(\begin{array}{c}n+k-1 \\ k\end{array}\right)=\left(\begin{array}{c}5+12-1 \\ 12\end{array}\right)=1820$[/tex]
Total of 1820 different kinds of banquets can be made
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