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Question

There are 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

A
91323
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B
232323
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C
120323
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D
None of these
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Solution

The correct option is A 91323Total ways =20P5Let x0= Number of sects to the left of the first person from the left.xi(1≤i≤4), the number of empty seats between the ith and (i+1)th person from left, and x5 the number of emply seats on the last person. x0≥0,x5≥0 and xi≥1 for 1≤i≤4x0+x1+...+x5=15= coefficient of x5 in (1+x+x2+...)2(x+x2+...)4=20−5+1C5=16C5Required probability 16C5.5!20P5=16P520P5=91323

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