17. Number of ways of selecting 3 people from 20 people sitting in a row such that no one of them are consecutive is

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Let $P_{n}$ denote the number of ways in which three people can be selected out of n people sitting in a row, if no two of them are consecutive. If, $P_{n + 1} - P_{n} = 15$ , then the value of n, is___.

Q. Let

P_{n}

denotes the number of ways in which three people can be selected out of

^{'} n^{'}

people sitting in a row, if no two of them are consecutive. If

P_{n + 1} - P_{n} = 15

then the value of

^{'} n^{'}

is :

Q. Let

P_{n}

denotes the number of ways of selecting 3 people out of

n

sitting in a row, if no two of them are consecutive and

Q_{n}

is the corresponding figure when they are in a circle. If

P_{n} - Q_{n} = 6

, then

n

is equal to

Thirteen persons are sitting in a row. Number of ways in which four persons can be selected so that no two of them are consecutive is also equal to

20

persons are sitting in a particular arrangement around a circular table. The number of ways of selection of three persons from them such that no two were sitting adjacent to each other is

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