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If 20cr = 20cr−10, Then 18cr is Equal to (A) 4896 (B) 816 (C) 1632 (D) Nont of These - Mathematics

MCQ

If 20Cr = 20Cr−10, then 18Cr is equal to

Options

  • 4896

  • 816

  • 1632

  •  nont of these

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Solution

816

\[r + r - 10 = 20\] [∵\[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
\[\Rightarrow 2r - 10 = 20\]
\[ \Rightarrow 2r = 30\]
\[ \Rightarrow r = 15\]
Now,
\[{}^{18} C_r =^{18} C_{15}\]
\[\therefore {}^{18} C_{15} = {}^{18} C_3\]
\[\therefore^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times 16 = 816\]
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 1 | Page 25
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