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

The number of words (with or without meaning) that can be formed from all the letters of the word "$LETTER$" in which vowels never come together is

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

There are three bags $B_1$,$B_2$,and $B_3$ containing $2$ Red and $3$ White,$5$ Red and $5$ White,and $3$ Red and $2$ White balls respectively. $A$ ball is drawn from bag $B_1$ and placed in bag $B_2$,then a ball is drawn from bag $B_2$ and placed in bag $B_3$,then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed,if the same colour balls are used in the first and second transfers (Assume all balls to be different) is

How many numbers are there between $100$ and $1000$ in which all the digits are distinct?

Number of ordered pairs $(x, y)$ of integers such that their product is a positive integer less than $100$ is -