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

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits such that the odd digits occupy even places?

Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is:

The total number of words that can be formed by using all the letters of the word $ALLEN$ such that all vowels occur in alphabetical order is:

The number lock of a suitcase has $4$ wheels,each labelled with ten digits,i.e.,from $0$ to $9$. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken $3$ at a time without repetition,such that each arrangement contains at least one vowel,is