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If 20cr = 20cr + 4 , Then Rc3 is Equal to (A) 54 (B) 56 (C) 58 (D) None of These - Mathematics

MCQ

If 20Cr = 20Cr + 4 , then rC3 is equal to

Options

  • 54

  •  56

  •  58

  • none of these

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Solution

 56

\[r + r + 4 = 20\] [∵\[{}^n C_x =^n C_y \Rightarrow n = x + y\ \text{or} x = y\]]
\[\Rightarrow 2r + 4 = 20\]
\[ \Rightarrow 2r = 16\]
\[ \Rightarrow r = 8\]
Now,
\[{}^r C_3 = {}^8 C_3\]
\[{}^8 C_3 = \frac{8!}{3! 5!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56\]
  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 2 | Page 25
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