# If 16cr = 16cr + 2, Find Rc4. - Mathematics

If 16Cr = 16Cr + 2, find rC4.

#### Solution

Given:

${}^{16} C_r = {}^{16} C_{r + 2}$
$16 = r + r + 2$  [∵ Property 5: ${}^n C_x = {}^n C_y \Rightarrow x = y$ or $x + y = n$
$\Rightarrow 2r + 2 = 16$
$\Rightarrow 2r = 14$
$\Rightarrow r = 7$
Now,
${}^r C_4 = {}^7 C_4$
$\Rightarrow {}^7 C_4 = {}^7 C_3$ [∵${}^n C_r =^n C_{n - r}$
$\Rightarrow^7 C_4 = {}^7 C_3 = \frac{7}{3} \times \frac{6}{2} \times \frac{5}{1} \times^4 C_0$
[∵${}^n C_r = \frac{n}{r} . {}^{n - 1} C_{r - 1}$]
$\Rightarrow^7 C_4 = 35$ [∵${}^n C_0 = 1$]
Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.1 | Q 14 | Page 8