If { }^{18} C_{r}={ }^{18} C_{r+2},find { }^{ | vedclass

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(A) Given that ${ }^{18} C_{r}={ }^{18} C_{r+2}$.We know the property ${ }^{n} C_{a}={ }^{n} C_{b}$ implies either $a=b$ or $a+b=n$.Here,$r 
eq r+2$,

Vedclass · Accepted Answer

$56$

Vedclass · Answer

(A) Given that ${ }^{18} C_{r}={ }^{18} C_{r+2}$.We know the property ${ }^{n} C_{a}={ }^{n} C_{b}$ implies either $a=b$ or $a+b=n$.Here,$r 
eq r+2$,so we must have $r + (r+2) = 18$.$2r + 2 = 18$$2r = 16$$r = 8$.Now,we need to find ${ }^{r} C_{5} = { }^{8} C_{5}$.${ }^{8} C_{5} = { }^{8} C_{8-5} = { }^{8} C_{3}$.${ }^{8} C_{3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 8 	imes 7 = 56$.

If ${ }^{18} C_{r}={ }^{18} C_{r+2}$,find ${ }^{r} C_{5}$.

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