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

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Question

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

Options

  • 4896

  • 816

  • 1632

  •  nont of these

MCQ
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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,
\[{}^{18} C_r =^{18} C_{15}\]
\[\therefore {}^{18} C_{15} = {}^{18} C_3\]
\[\therefore^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times 16 = 816\]
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Chapter 17: Combinations - Exercise 17.5 [Page 25]

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R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.5 | Q 1 | Page 25

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