# If 15c3r = 15cr + 3, Find R. - Mathematics

If 15C3r = 15Cr + 3, find r.

#### Solution

Given:
15C3r = 15Cr + 3

$15 = 3r + r + 3 .$  [∵${}^n C_x = {}^n C_y \Rightarrow x = y$] or, $n = x + y$
$\Rightarrow 15 = 4r + 3$
$\Rightarrow 4r = 12$
$\Rightarrow r = 3$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.1 | Q 7 | Page 8