How many numbers between $999$ and $10,000$ can be formed using the digits $0, 2, 3, 6, 7, 8$ without repetition?

The number of words that can be formed by using the letters of the word $CALCULATE$ such that each word starts and ends with a consonant,are

The number of seven-digit odd numbers that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is $.......$

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?

How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

All the letters of the word $LETTER$ are arranged in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order. Then the rank of the word $TETLER$ is