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Question
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
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Solution
5 boys can be seated among themselves in 5P5 = 5! Ways. After this arrangement, we have to arrange the three girls in such a way that in between two girls there atleast one boy.
So the possible places girls can be placed with the × symbol given below.
× B × B × B × B × B ×
∴ There are 6 places to seated by 3 girls which can be done 6P3 ways.
∴ Total number of ways = 5! × 6P3
= 120 × (6 × 5 × 4)
= 120 × 120
= 14400
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