Question

which two terms represent the number of groups of three players that are all juniors? ₁₄c₃ 20 ₁₄c₆ 3,003 ₆c₃ 364

Explanation:

Step1: Identify combination formula

The number of ways to choose 3 juniors from 6 juniors is given by the combination formula $_{n}\text{C}_{k}=\frac{n!}{k!(n-k)!}$, where $n=6$ and $k=3$.

Step2: Calculate $_{6}\text{C}_{3}$

$$\begin{align*} _{6}\text{C}_{3}&=\frac{6!}{3!(6-3)!}\\ &=\frac{6\times5\times4\times3!}{3!\times3\times2\times1}\\ &=\frac{6\times5\times4}{3\times2\times1}\\ &=20 \end{align*}$$

Answer:

• $_{6}\text{C}_{3}$
• 20