Find the value of $^{10} C_{3}$

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Solution

$^{10} C_{3} = ?$
$⌊^{n} C_{r} = \frac{n!}{r! (n - r)!} ⌋ \Rightarrow \frac{10!}{3! \times 7!} = \frac{10 \times 9 \times 8}{3 \times 2} = 120 \Rightarrow^{10} C_{3} = 120$
Hence the correct answer is $120$

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