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Evaluate the Following:12c10 - Mathematics

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Evaluate the following:

12C10

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Solution

We have,

\[{}^{12} C_{10} =^{12} C_2\]         [∵\[{}^n C_r = {}^n C_{n - r}\]]
\[\Rightarrow {}^{12} C_{10} =^{12} C_2 = \frac{12}{2} \times \frac{11}{1} \times^{{}^{10}} C_0\]  [∵\[{}^n C_r = \frac{n}{r} {}^{n - 1} C_{r - 1}\]]
\[\Rightarrow^{12} C_{10} = \frac{12}{2} \times \frac{11}{1} \times 1\]    [∵\[{}^n C_0 = 1\]]
\[\Rightarrow^{12} C_{10} = 66\]
Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.1 | Q 1.2 | Page 8

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