Sweater

Dana confuses sweater and wool has a choice of seven colors. In how many ways she can choose from three colors to the sleeves?

Correct result:

n1 =  35
n2 =  210

Solution:

$C_{{ 3}}(7)=\dbinom{ 7}{ 3}=\dfrac{ 7! }{ 3!(7-3)!}=\dfrac{ 7 \cdot 6 \cdot 5 } { 3 \cdot 2 \cdot 1 }=35 \ \\ \ \\ n_{1}={ { 7 } \choose 3 }=35$
$n_{2}=7 \cdot \ 6 \cdot \ 5=210$

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