Given a box with 5 color pencils:
How many different sets of 3 pencils can be chosen from it
Let the total pencil be n
and the different sets of pencils be r
[tex]\begin{gathered} nC_r \\ 5C_3 \end{gathered}[/tex][tex]\begin{gathered} 5C_3=\frac{5!}{(5-3)!3!} \\ =\frac{5!}{2!3!} \\ =\frac{5\times4\times3!}{2\times3!} \\ =\frac{20}{2} \\ =10 \end{gathered}[/tex]Therefore the 3 different sets of pencils can be chosen in 10 ways
Hence the correct answer is Option C
