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If 8cr − 7c3 = 7c2, Find R. - Mathematics

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If 8Cr − 7C3 = 7C2, find r.

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Solution

Given:
 8Cr − 7C3 = 7C2
We have,\[{}^8 C_r = {}^7 C_2 + {}^7 C_3\]

\[\Rightarrow {}^8 C_r =^8 C_3\] [∵\[{}^n C_r + {}^n C_{r - 1} = {}^{n + 1} C_r\]]
\[r \leq n\]
\[\Rightarrow r = 3\] [∵\[{}^n C_x = {}^n C_y \Rightarrow x = y\]]  or,\[n = x + y\]
\[\text{And}r + 3 = 8\]
\[ \Rightarrow r = 5\]
Concept: Combination
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APPEARS IN

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

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