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Question

If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is


A

85

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B

100

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C

120

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D

240

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Solution

The correct option is C

120


Explanation for correct option:

Finding the possibilities:

Given, total 12 persons are seated in a row.

The number of ways for selecting 3 persons from 12 people under the given data.

The Number of ways of arranging 3 people from 9 people seated in a row, in such a way that no two of them are consecutive.

= Number of ways of arranging 3 places from 10

=C310

=10!10-3!3!

=10×9×8×7!7!×1×2×3

=120

Hence, correct answer is option C


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