The number of arrangements of the letters of the word $INDEPENDENCE$ in which all the vowels always occur together is

How many $4$-letter codes can be formed using the first $10$ letters of the English alphabet,if no letter can be repeated?

If $^{12}P_r = 1320$,then $r$ is equal to

How many $6$-digit numbers can be formed using only odd digits,such that all odd digits appear at least once?

For $n = 1, 2, 3, . . . , 50$,let $A = \{ a_n \mid a_n = \begin{cases} (-1)^{\frac{n}{2}} (\frac{n}{2}), & \text{if } n \text{ is even} \\ (-1)^{\frac{n-1}{2}} (\frac{n-1}{2}), & \text{if } n \text{ is odd} \end{cases} \}$ and $B$ be the set of all distinct elements of $A$. The number of permutations of all the elements of set $B$ such that even integers are in increasing order is:

There are $5$ roads from a village to a city. In how many different ways can a villager go to the city and return back?