In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ?

Question

In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ? (A) 4! (B) 5! (C) 4! + 5! (D) 4! × 5!

Tardigrade Admin · Accepted Answer

Leaving one seat vacant between two boys, 5 boys may be seated in 4 ! ways. Then at remaining 5 seats, 5 girls any sit in 5 ! ways. Hence the required number =4 ! × 5 !

Q. In how many ways can $5$ boys and $5$ girls be seated at a round table so that no two girls may be together ?

$4!$

$5!$

$4! + 5!$

$4! \times 5!$

Leaving one seat vacant between two boys, $5$ boys may be seated in $4!$ ways. Then at remaining $5$ seats, $5$ girls any sit in $5!$ ways.
Hence the required number $= 4! \times 5!$

Q. In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ?

4!

5!

4!+5!

4!×5!