Since order is not important, the combination may be used. The formula is as follows.
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]where n is the number of possible options and r is the number of chosen options.
Thus, the given are as follows.
[tex]\begin{gathered} n=12 \\ r=5 \end{gathered}[/tex]Substitute the given values into the formula and then simplify.
[tex]\begin{gathered} _{12}C_5=\frac{12!}{5!(12-5)!} \\ =\frac{12!}{5!(7)!} \\ =\frac{(12)(11)(10)(9)(8)(7!)}{(5!)(7!)} \\ =\frac{(12)(11)(10)(9)(8)}{120} \\ =\frac{95040}{120} \\ =792 \end{gathered}[/tex]Therefore, there must be 792 ways.
