How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many $3$-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

The sum of the digits in the unit's place of all the $4-$ digit numbers formed by using the digits $3, 4, 5,$ and $6$,without repetition,is:

The number of natural numbers less than $1000$,in which no two digits are repeated,is:

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ if $L$ and $P$ are always excluded?