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Question

# There are 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:

A
7C4
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B
4.7P3
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C
7C34!
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D
840
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Solution

## The correct option is D 840x––1 y–1 z–1 w––1u––− represents empty seat represents one personx+1+y+1+2+1+w+1+u=10x+y+z+w+u=6x,u≥0 and y,z,w>0∴x+y+z+w+u=3x,y,z,w,u≥3Number of ways =(5+(3−1))!(5−1)(3)! =7!4!3!=7!4!3!∴ total number of arrangements=7!4!3!.4!→ Arrange of people=7C4.4!=840

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