# 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

#### 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,
${}^r C_3 = {}^8 C_3$
${}^8 C_3 = \frac{8!}{3! 5!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$
Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 2 | Page 25