$A$ 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.

In how many ways can a team of $11$ members be formed from a group of $15$ persons?

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

For a scholarship,at most $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selecting at least one candidate for the scholarship is $63$,then the maximum number of candidates that can be selected for the scholarship is -