If $a, b$ and $c$ are the greatest value of $^{19} \mathrm{C}_{\mathrm{p}},^{20} \mathrm{C}_{\mathrm{q}}$ and $^{21 }\mathrm{C}_{\mathrm{r}}$ respectively, then
$\frac{a}{11}=\frac{b}{22}=\frac{c}{21}$
$\frac{\mathrm{a}}{10}=\frac{\mathrm{b}}{11}=\frac{\mathrm{c}}{21}$
$\frac{\mathrm{a}}{10}=\frac{\mathrm{b}}{11}=\frac{\mathrm{c}}{42}$
$\frac{a}{11}=\frac{b}{22}=\frac{c}{42}$
An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is
How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$
If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
at most $3$ girls?
If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-