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

How many words can be formed using the letters of the word $COURTESY$ such that the first letter is $C$ and the last letter is $Y$?

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose the chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is:

On the occasion of the Deepawali festival,each student of a class sends greeting cards to every other student. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ is: