The number of ways in which ten candidates $A_1, A_2, \dots, A_{10}$ can be ranked such that $A_1$ is always above $A_{10}$ is:

In how many ways can the letters of the word $TRIANGLE$ be arranged such that no two vowels occur together?

The number of permutations by taking all letters and keeping the vowels of the word $COMBINE$ in the odd places is

The numbers $1, 2, 3,$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. $A$ person draws two slips from the box,one after the other,without replacement. Describe the sample space for the experiment.

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

If the different permutations of all the letters of the word $EXAMINATION$ are listed as in a dictionary,how many words are there in this list before the first word starting with $E$?