How many numbers less than $1000$ can be made from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

$A$ 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.

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

In an election,the number of candidates is $1$ greater than the number of persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can be selected from this group such that there is at least one boy and at least one girl in each team is $1750$,then $n$ is equal to:

If $^{56}P_{r+6} : ^{54}P_{r+3} = 30800 : 1$,then $r = $