Question

Evaluate the following:

¹²C₁₀

Answer 1

We have,

\[{}^{12} C_{10} =^{12} C_2\]         [∵\[{}^n C_r = {}^n C_{n - r}\]]

\[\Rightarrow {}^{12} C_{10} =^{12} C_2 = \frac{12}{2} \times \frac{11}{1} \times^{{}^{10}} C_0\]  [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]

\[\Rightarrow^{12} C_{10} = \frac{12}{2} \times \frac{11}{1} \times 1\]    [∵\[{}^n C_0 = 1\]]

\[\Rightarrow^{12} C_{10} = 66\]