In how many ways can the letters of the word '$UNIVERSAL$' be arranged when $E, R, S$ are always together?

$A$ code word is to consist of $2$ English alphabets followed by $2$ distinct numbers between $1$ and $9$. For example,$CA23$ is a code word. How many such code words are there?

Each section in the first year of a plus $2$ course has exactly $40$ students. If there are $5$ sections,in how many ways can a set of $4$ student representatives be selected,$1$ from each section?

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee should have all $4$ professors and $1$ research associate $OR$ all $3$ trainees and $2$ professors?