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If 15cr : 15cr − 1 = 11 : 5, Find R. - Mathematics

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If 15Cr : 15Cr − 1 = 11 : 5, find r.

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Solution

Given:
 15Cr : 15Cr − 1 = 11 : 5
We have,

\[\frac{{}^{15} C_r}{{}^{15} C_{r - 1}} = \frac{11}{5}\]

\[\Rightarrow \frac{15 - r + 1}{r} = \frac{11}{5}\]
\[\frac{{}^n C_r}{{}^n C_{r - 1}} = \frac{n - r + 1}{r}\]

\[\Rightarrow 75 - 5r + 5 = 11r\]
\[ \Rightarrow 16r = 80\]
\[ \Rightarrow r = 5\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.1 | Q 9 | Page 8

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