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

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

How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

The total number of words that can be formed using the letters $a, b, c, d, e, f$ taken $3$ at a time such that each word contains at least one vowel 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: