Five boys and five girls are writing an examination in a hall in which 5 benches are arranged in a row and only two students are to be seated on every bench at either of its ends. If the seating arrangement is to be such that no two boys or no two girls sit together as neighbours (a student should not have a student of same gender either on left or right; immediate front or back), then the total number of such arrangements is

Question

Five boys and five girls are writing an examination in a hall in which 5 benches are arranged in a row and only two students are to be seated on every bench at either of its ends. If the seating arrangement is to be such that no two boys or no two girls sit together as neighbours (a student should not have a student of same gender either on left or right; immediate front or back), then the total number of such arrangements is (A) 28800 (B) 14400 (C) 240 (D) 480

Tardigrade Admin · Accepted Answer

Total number of such arrangements =( 5 C5 × 5 P5) ×( 5 C5 × 5 P5) × 2 ! =5 ! × 5 ! × 2 !=120 × 120 × 2=28800

28800

14400

240

480

Total number of such arrangements =(5C5​×5P5​)×(5C5​×5P5​)×2! =5!×5!×2!=120×120×2=28800

Total number of such arrangements
$= (^{5} C_{5} \times^{5} P_{5}) \times (^{5} C_{5} \times^{5} P_{5}) \times 2!$
$= 5! \times 5! \times 2! = 120 \times 120 \times 2 = 28800$