Question

If 18Cr

= 18Cr+2, the value of r

C5 is​

Answer 1

There is properties that

Answer 2

The value of $^rC_5$ is 56.

Step-by-step explanation:

It is given that

$^{18}C_r=^{18}C_{r+2}$

We know that if $^nC_p=^nC_q$

then p=q or p+q=n, where n, p and q are whole numbers.

For the given statement

$r\neq r+2$ So,

$r+(r+2)=18$

$2r+2=18$

$2r=18-2$

$2r=16$

Divide both sides by 2.

$r=8$

We need to find the value of $^rC_5$.

$^rC_5=^8C_5=\dfrac{8!}{5!(8-5)!}=\dfrac{8\cdot 7\cdot 6\cdot 5!}{5!\cdot 3\cdot 2\cdot 1}=56$

Therefore, the value of $^rC_5$ is 56.

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If 18Cr = 18Cr+2, the value of rC5 is​

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