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 numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

How many numbers of four digits can be formed with the digits $1, 2, 3, 4$ and $5$?

How many $5$-digit even numbers can be formed using the digits $1, 2, 5, 5, 4$?

$A$ customer forgets a $4$-digit code for an Automatic Teller Machine ($A$.$T$.$M$.) in a bank. However,he remembers that this code consists of digits $3, 5, 6$ and $9$. Find the largest possible number of trials necessary to obtain the correct code.

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is: