$^n{P_r}{ \div ^n}{C_r}$ =
$n\,!$
$(n - r)!$
$\frac{1}{{r!}}$
$r\,!$
A total number of words which can be formed out of the letters $a,\;b,\;c,\;d,\;e,\;f$ taken $3$ together such that each word contains at least one vowel, is
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-
If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$
If ${ }^{2n } C _3:{ }^{n } C _3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is