How many numbers can be formed using the digits $1, 2, 3, 4, 3, 2, 1$ such that odd digits always occupy odd positions?

The number of all four-digit numbers that can be formed with the digits $0, 1, 2, 3, 4, 5$ when the repetition of the digits is not allowed,is

Let $b_{1} b_{2} b_{3} b_{4}$ be a $4$-element permutation with $b_{i} \in \{1, 2, 3, \ldots, 100\}$ for $1 \leq i \leq 4$ and $b_{i} \neq b_{j}$ for $i \neq j$,such that either $b_{1}, b_{2}, b_{3}$ are consecutive integers or $b_{2}, b_{3}, b_{4}$ are consecutive integers. Find the number of such permutations.

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels do not occur together.

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

The sum of the units digits of all numbers formed using the digits $3, 4, 5, 6$ without repetition is......