SOLUTION
The question involves combination since it only deals with the selection without arrangement.
Hence the formula to use is
[tex]^nC_r=\frac{n!}{(n-r)!r}[/tex]For this question, we have
[tex]\begin{gathered} n=15,r=5 \\ ^nC_r=\frac{n!}{(n-r)!r} \\ \text{becomes } \\ ^{15}C_5=\frac{15!}{(15-5)!5!} \end{gathered}[/tex]Simplifying the last expression we obtained
[tex]\begin{gathered} ^{15}C_5=\frac{15!}{10!5!} \\ =\frac{15\times14\times13\times12\times11\times10!}{10!\times5!} \\ =3003 \end{gathered}[/tex]Therefore,
The number of committees to be chosen is 3003
