The number of all four-digit numbers which do not have four distinct digits is

In how many ways can $n$ prizes be distributed among $n$ boys such that no boy gets all the prizes?

$A$ person forgets his $4-$digit $ATM$ pin code. But he remembers that in the code all the digits are different,the greatest digit is $7$ and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is $...........$.

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

The remainder obtained when $1! + 2! + 3! + \ldots + 11!$ is divided by $12$ is

The number of $6$-letter words,with or without meaning,that can be formed using the letters of the word $\text{MATHS}$ such that any letter that appears in the word must appear at least twice,is $...$