Sweater

Dana confuses me by stating that sweaters and wool have a choice of seven colors. How many ways can she choose from three colors for the sleeves?

Correct answer:

n₁ =  35
n₂ =  210

Step-by-step explanation:

$$\begin{gathered} C_3(7)=\left(\genfrac{}{}{0ex}{}{7}{3}\right)=\frac{7!}{3!(7-3)!}=\frac{7\cdot 6\cdot 5}{3\cdot 2\cdot 1}=35 \\ {n}_1=\left(\genfrac{}{}{0ex}{}{7}{3}\right)=35 \end{gathered}$$

$n_2=7\cdot 6\cdot 5=210$

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