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?

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,seven of which lie on the same straight line,is

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

$A$ dictionary is printed consisting of $7$-letter words only that can be formed using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

The number of words that can be formed out of the letters of the word $ARTICLE$ so that the vowels occupy even places is