Compute $\frac{7!}{5!}$

The number of six-letter words (with or without meaning) formed using all the letters of the word $VOWELS$ such that all the consonants never come together is ... .

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is:

In how many ways can $6$ examination papers be arranged so that the best and the worst papers are never together?

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?

If all the letters of the word $MASTER$ are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order,then the rank of the word $MASTER$ is