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-
$1320$
$1560$
$1800$
$1740$
Out of $10$ white, $9$ black and $7$ red balls, the number of ways in which selection of one or more balls can be made, is
The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals
If the number of five digit numbers with distinct digits and $2$ at the $10^{\text {th }}$ place is $336 \mathrm{k}$, then $\mathrm{k}$ is equal to
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
The solution set of $^{10}{C_{x - 1}} > 2\;.{\;^{10}}{C_x}$ is