If a, b and c are the greatest values of ^{19 | vedclass

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(D) The greatest value of $^{n}C_{r}$ occurs at $r = \frac{n}{2}$ if $n$ is even,and at $r = \frac{n-1}{2}$ or $r = \frac{n+1}{2}$ if $n$ is odd.For $

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$\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$

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(D) The greatest value of $^{n}C_{r}$ occurs at $r = \frac{n}{2}$ if $n$ is even,and at $r = \frac{n-1}{2}$ or $r = \frac{n+1}{2}$ if $n$ is odd.For $a = ^{19}C_{p}$,the greatest value is at $p = 9$ or $10$,so $a = ^{19}C_{9} = ^{19}C_{10}$.For $b = ^{20}C_{q}$,the greatest value is at $q = 10$,so $b = ^{20}C_{10}$.For $c = ^{21}C_{r}$,the greatest value is at $r = 10$ or $11$,so $c = ^{21}C_{10} = ^{21}C_{11}$.Using the property $^{n}C_{r} = \frac{n}{r} \cdot ^{n-1}C_{r-1}$:$b = ^{20}C_{10} = \frac{20}{10} \cdot ^{19}C_{9} = 2a$.$c = ^{21}C_{10} = \frac{21}{11} \cdot ^{20}C_{10} = \frac{21}{11}b = \frac{21}{11}(2a) = \frac{42a}{11}$.Thus,$a : b : c = a : 2a : \frac{42a}{11} = 11 : 22 : 42$.This implies $\frac{a}{11} = \frac{b}{22} = \frac{c}{42}$.

If $a, b$ and $c$ are the greatest values of $^{19}C_{p}, ^{20}C_{q}$ and $^{21}C_{r}$ respectively,then

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