Find the value of \binom{10}{3} (10 choose 3).

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{"type":"doc","content":[{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"text":" The formula for combinations (binomial coefficients) is:","type":"text"}]},{"attrs":{"latex":"\binom{n}{k} = \frac{n!}{k!(n-k)!} = \frac{n \times (n-1) \times \dots \times (n-k+1)}{k \times (k-1) \times \dots \times 1}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2:","type":"text"},{"text":" Substitute ","type":"text"},{"attrs":{"latex":"n = 10"},"type":"math_inline"},{"text":" and ","type":"text"},{"type":"math_inline","attrs":{"latex":"k = 3"}},{"text":":","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1}"},"type":"math_block"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 3:"},{"type":"text","text":" Simplify the fraction:"}],"type":"paragraph"},{"type":"math_block","attrs":{"latex":"\binom{10}{3} = \frac{720}{6} = 120"}},{"content":[{"type":"text","text":"So "},{"type":"math_inline","attrs":{"latex":"\binom{10}{3} = 120"}},{"text":".","type":"text"}],"type":"paragraph"}]}

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