Find the number of ways in which two Americans, two British, One Chinese, One Dutch and one Egyptian can sit on a round table so that person of the same nationality are separated?
$330$
$240$
$336$
$422$
In how many ways can the letters of the word $\mathrm{ASSASSINATION} $ be arranged so that all the $\mathrm{S}$ 's are together?
The least value of a natural number $n$ such that $\left(\frac{n-1}{5}\right)+\left(\frac{n-1}{6}\right) < \left(\frac{n}{7}\right)$, where $\left(\frac{n}{r}\right)=\frac{n !}{(n-r) ! r !}, i$
In an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is
A country has ten smart cities. The government decides to connect all these cities by road. How many roads the government need to construct so that every city is connected to every other city ?
In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation