Question

if 21 CR is equal to 21 CR plus 3 then find rc6
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Answer 1

Step-by-step explanation:

Solution(By Examveda Team). 15 is a superscript of C and 3r, r+3 are subscripts of C. If 15C3r = 15Cr+ 3 , then we follow the formula:

Hope you understand -!

Answer 2

The value of $^{r}C_{6}$ is 84.

Given:

$^{21}C_{r}$=   $^{21}C_{r+3}$

To find:

The value of $^{r}C_{6}$.

Solution:

$^{21}C_{r}$=   $^{21}C_{r+3}$

Since, for ⁿCₐ= ⁿCₓ

n= a+x

Similarly, for $^{21}C_{r}$=   $^{21}C_{r+3}$

21= r+r+3

2r= 18

r= 9

Now, put the value of r in $^{r}C_{6}$.

$^{r}C_{6}$= ⁹C₆

Here, we can put the formula

$^{n}C_{r}$= $\frac{n!}{(n-r)!r!}$

So, ⁹C₆= $\frac{9!}{6!(9-6)!}$

⁹C₆=  $\frac{9!}{6! 3!}$

⁹C₆=  $\frac{(9)(8)(7)6!}{6!(1)(2)(3)}$

⁹C₆=  4×3×7

⁹C₆=  84

Therefore, the value of  $^{r}C_{6}$ is 84.

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