The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is

Question

The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is (A) 14040 (B) 14440 (C) 14000 (D) 14400

Tardigrade Admin · Accepted Answer

5 girls can be arranged in 5 !=120 ways 3 boys between 5 girls with positions can be arranged in 6 P 3=6 ⋅ 5 ⋅ 4=120 ways ∴ Total number of arrangements =120 × 120=14400

Q. The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is

14040

14440

14000

14400

5 girls can be arranged in $5! = 120$ ways
3 boys between 5 girls with positions can be arranged in $^{6} P_{3} = 6 \cdot 5 \cdot 4 = 120$ ways
$∴$ Total number of arrangements $= 120 \times 120 = 14400$

Q. The number of ways in which 5 girls and 3 boys can be seated in a row so the no two boys are together is

14040

14440

14000

14400

5 girls can be arranged in 5!=120 ways 3 boys between 5 girls with positions can be arranged in 6P3​=6⋅5⋅4=120 ways ∴ Total number of arrangements =120×120=14400

5 girls can be arranged in $5! = 120$ ways
3 boys between 5 girls with positions can be arranged in $^{6} P_{3} = 6 \cdot 5 \cdot 4 = 120$ ways
$∴$ Total number of arrangements $= 120 \times 120 = 14400$