If a, b and c are the greatest values of ^19C_p, ^20C_q and ^21C_r respectively, then:

Question

If $a$, $b$ and $c$ are the greatest values of $^{19}C_p$, $^{20}C_q$ and $^{21}C_r$ respectively, then:

Accepted Answer

$^nC_r$ is greatest at the middle term(s): $a={}^{19}C_9={}^{19}C_{10}$, $b={}^{20}C_{10}$, $c={}^{21}C_{10}={}^{21}C_{11}$.

$$\frac{a}{1} : \frac{b}{2\cdot\frac{20}{10}\cdot\ldots}$$

Using ratios $\dfrac{b}{a} = \dfrac{^{20}C_{10}}{^{19}C_9} = 2$, and $\dfrac{c}{a}=\dfrac{^{21}C_{11}}{^{19}C_9}=\dfrac{42}{11}$:

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

Solutions · 1