The number of $7$ digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is

How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

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 of arranging all the letters of the word $PERFECTION$ such that there must be exactly two consonants between any two vowels is

The number of words,with or without meaning,that can be formed by taking $4$ letters at a time from the letters of the word $'SYLLABUS'$ such that two letters are distinct and two letters are alike,is

How many arrangements can be made using the letters of the word $CALCUTTA$?