The numbers can be formed using the digits $$1,2,3,4,3,2,1$$ so that odd digits always occupy odd places in __________ ways.

A polygon has 44 diagonals. Then the number of sides of the polygon are

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is

The number of ways in which 8 different pearls can be arranged to form a necklace is