Question

A box contains 5 color pencils. How many different sets of 3 pencils can be chosen from it?A. 6B. 20C. 10D. 4

Answer 1

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

`\begin{gathered} nC_r \\ 5C_3 \end{gathered}`
`\begin{gathered} 5C_3=(5!)/((5-3)!3!) \\ =(5!)/(2!3!) \\ =(5*4*3!)/(2*3!) \\ =(20)/(2) \\ =10 \end{gathered}`

Therefore the 3 different sets of pencils can be chosen in 10 ways

Hence the correct answer is Option C