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There are 10 seats in the first row of a theatre of which 4 ar

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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:

_{7} C_{4}

4._{7} P_{3}

_{7} C_{3} 4!

840

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Eleanor Discussed

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:

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

\underline{x} 1

\underline{y} 1

\underline{z} 1

\underline{w} 1 \underline{u}

-

represents empty seat

represents one person

x + 1 + y + 1 + 2 + 1 + w + 1 + u = 10

x + y + z + w + u = 6

x, u \geq 0

and

y, z, w > 0

∴ x + y + z + w + u = 3

x, y, z, w, u \geq 3

Number of ways

= \frac{( 5 + ( 3 - 1 ))!}{( 5 - 1 ) ( 3 )!}

= \frac{7 !}{4 ! 3 !} = \frac{7 !}{4 ! 3 !}

∴

total number of arrangements

= \frac{7 !}{4 ! 3 !} . 4! \to

Arrange of people

=^{7} C_{4} .4!

= 840

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Question Text	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:
Answer Type	Text solution:1
Upvotes	151