Answer
$35$
Work Step by Step
RECALL:
${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$
Use the formula above to obtain:
${7}\choose{3}$$\require{cancel}=\dfrac{7!}{3!(7-3)!}=\dfrac{7!}{3!4!}=\dfrac{7\cdot 6 \cdot 5\cdot 4\cdot 3 \cdot 2 \cdot 1}{(3\cdot 2 \cdot 1) (4\cdot 3 \cdot 2 \cdot 1)}=\dfrac{7\cdot \cancel{6} \cdot 5\cdot \cancel{4\cdot 3 \cdot 2 \cdot 1}}{(\cancel{3\cdot 2} \cdot 1) \cancel{(4\cdot 3 \cdot 2 \cdot 1)}}=35$
