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 an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is
The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is
There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84,$ then the value of $m$ is
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
The value of ${}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}{C_3}} $ is