How many words can be formed using the letters of the word $COMMITTEE$?

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

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to

The number of odd numbers greater than $6,00,000$ that can be formed by using the digits $3, 6, 7, 8, 9, 0$ without repetition is

The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.

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: