How many words,with or without meaning,each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

There are $10$ students in a classroom,including $3$ girls $A, B,$ and $C$. In how many ways can they be arranged in a row such that no two of the three girls are together?

How many numbers greater than $1000000$ can be formed by using the digits $1, 2, 0, 2, 4, 2, 4$?

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?

The number of ways in which all the letters of the word $COMBINATION$ can be arranged so that the vowels always come together is: