There are $6$ multiple choice questions on an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next $3$ have $5$ each?

$^nC_r \div ^nC_{r-1} = $

There are $3$ sections in a question paper and each section contains $5$ questions. $A$ candidate has to answer a total of $5$ questions,choosing at least one question from each section. Then the number of ways,in which the candidate can choose the questions,is

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

The number of ways in which $5$ beads of different colours form a necklace is