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

Find $n$ if ${ }^{n} P_{4}=18 \cdot{ }^{n-1} P_{2}$.

The number of diagonals in an octagon is:

In an examination,Yamini has to select $4$ questions from each part. There are $6, 7,$ and $8$ questions in Part-$I,$ Part-$II,$ and Part-$III,$ respectively. What is the number of possible combinations in which she can choose the questions?

$^{n - 1}C_r = (k^2 - 3) \cdot ^nC_{r + 1}$ if $k \in$

In how many different ways can the letters of the word '$DETAIL$' be arranged in such a way that the vowels occupy only the odd positions?