What is the probability that the two $E$'s come together in the words formed by the letters of the word $PEACE$?

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:

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?