The number of ways in which 4 boys and 4 girls can be arranged in a ro

1.	The number of ways in which 4 boys and 4 girls can be arranged in a row so that no two girls and no two boys are together is1. (4!)22. 2(4!)23. 8!4. None of these
Answer» Correct Answer - Option 2 : 2(4!)2 Calculation: Given: 4 boys and 4 girls can be arranged in a row so that no two girls and no two boys are together. It means they can sit alternately Case-I: 1st person in the row is a boy. B₁G₁B₂G₂B₃G₃B₄G₄ The no. of ways in which the boys can be rearranged among themselves is 4!. Similarly, The no. of ways in which the girls can be rearranged among themselves is 4!. So, the total number of ways = 4! × 4! = (4!)² Case-II:1st person in the row is a girl. G1B₁G2B2G₃B₃G₄B₄ The no. of ways in which the girls can be rearranged among themselves is 4!. Similarly, The no. of ways in which the boys can be rearranged among themselves is 4!. So, the total number of ways = 4! × 4! = (4!)² Hence, Total Number of ways = (4!)2 + (4!)2 = 2(4!)2

The number of ways in which 4 boys and 4 girls can be arranged in a row so that no two girls and no two boys are together is1. (4!)22. 2(4!)23. 8!4. None of these

Answer» Correct Answer - Option 2 : 2(4!)2

Calculation:

Given: 4 boys and 4 girls can be arranged in a row so that no two girls and no two boys are together.

It means they can sit alternately

Case-I: 1st person in the row is a boy.

B₁G₁B₂G₂B₃G₃B₄G₄

The no. of ways in which the boys can be rearranged among themselves is 4!.
Similarly, The no. of ways in which the girls can be rearranged among themselves is 4!.
So, the total number of ways = 4! × 4! = (4!)²

Case-II:1st person in the row is a girl.

G1B₁G2B2G₃B₃G₄B₄

The no. of ways in which the girls can be rearranged among themselves is 4!.
Similarly, The no. of ways in which the boys can be rearranged among themselves is 4!.
So, the total number of ways = 4! × 4! = (4!)²

Hence, Total Number of ways = (4!)2 + (4!)2 = 2(4!)2

The number of ways in which 4 boys and 4 girls can be arranged in a row so that no two girls and no two boys are together is1. (4!)22. 2(4!)23. 8!4. None of these

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