1.

In the case of circular permutation, n different objects can be arranged in (n-1)! number of ways.

Hence if the number of people are five, they are like five different objects.

Accordingly they can be seated around a circular table in (5-1)! number of ways,

Or 4! number of ways

= 4.3.2.1

=24 ways

2.

The word ELATION has 7 alphabets, which are all different.

The arrangement of words in this case is like 7 rectangular boxes being filled with one alphabet each.

The first box can be filled in 7ways and then having filled the first box, the second box can be filled in 6 ways and so on.

By applying the fundamental principal of counting the total number of ways will be 7.6.5.4.3.2.1

=5040

Hence the total number of words that can be formed are 5040

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