Answer
$21$
Work Step by Step
RECALL:
${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$
Use the formula above to obtain:
${7}\choose{5}$$\require{cancel}
\\=\dfrac{7!}{5!(7-5)!}
\\=\dfrac{7!}{5!2!}
\\=\dfrac{7\cdot 6 \cdot 5\cdot 4\cdot 3 \cdot 2 \cdot 1}{(5\cdot4\cdot 3\cdot 2 \cdot 1) (2 \cdot 1)}
\\=\dfrac{7\cdot \cancel{6}^3 \cdot \cancel{5\cdot 4\cdot 3 \cdot 2 \cdot 1}}{\cancel{(5\cdot4\cdot 3\cdot 2 \cdot 1)} (\cancel{2} \cdot 1)}
\\=21$
