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Inequality in the US

23. There are...

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23. There are 7 seats in a row. Three persons take seats at random . The prob that the middle seat is occupied and no two persons are consecutive

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Q. There are 7 seats in a row. Three persons take seats at random. The probability that the middle seat is always occupied and no two persons are consecutive is

Q. There are m seats in the first row of a theatre of which n are to be occupied. Number of ways of arranging n persons so that there should be at least two empty seats between any two persons

Q. There are 12 seats in a row of a cinema theatre which is nearer to the entrance. 4 persons enter the theatre and occupy the seats in that row (Before their entry the seats are vacant). If

n_{1}

is the number of ways in which they occupy the seats, such that no two persons are together and

n_{2}

is the number of ways in which each person has exactly one neighbour

n_{1} : n_{2}

10

seats in the first row of a theatre of which

4

are to be occupied. The number of ways of arranging

4

persons so that no two persons sit side by side is:

20

seats in some row of a movie theatre and

5

persons sit randomly in this row. The probability that no two persons sit side by side, is

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