The number of ways in which the letters of the word $TRIANGLE$ can be arranged such that two vowels do not occur together is

If the letters of the word $MOTHER$ are permuted and all the words so formed (with or without meaning) are listed as in a dictionary,then the position of the word $MOTHER$ is

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to

How many words,with or without meaning,can be formed using the letters of the word $MONDAY$,assuming that no letter is repeated,if all letters are used but the first letter is a vowel?

Let $b_{1} b_{2} b_{3} b_{4}$ be a $4$-element permutation with $b_{i} \in \{1, 2, 3, \ldots, 100\}$ for $1 \leq i \leq 4$ and $b_{i} \neq b_{j}$ for $i \neq j$,such that either $b_{1}, b_{2}, b_{3}$ are consecutive integers or $b_{2}, b_{3}, b_{4}$ are consecutive integers. Find the number of such permutations.

Three children,each accompanied by a guardian,seek admission in a school. The principal wants to interview all the $6$ persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?