In how many ways can 5girls and 3 boys be seated in a row so that no two boys are together

Here In the question, there are 5 girls. 5 girls can be seated in ^{5}P_{5}=5x4x3x2x1=5! ways. After arranging the girls in 5 ways, boy can sit in 6 places, as given below by **$** sign:

**$** G** $ **G**$** G** $** G** $** G **$**

Now, the question says that no two boys can sit togerher. So there are 6 places where these 3 boys can sit. So now the boys can sit in ^{6}P_{3.}

Therefore, the total number of seating arrangements possible

=^{5}P_{5} x ^{6}P_{3 }

= 5 x 4 x 3 x 2 x 1 x 6 x 5 x 4 ways

=**14400 ways**

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