Question

In how many ways can $5$ girls and $3$ boys stand in a row so that no $2$ boys are together?

• A. $14560$
• B. $14300$
• C. $14400$
• D. $16400$

Answer 1

Answer: (C)

$14400$

FIVE GIRLS CAN be placed in $5!$ ways

set the positions for girls first $-g-g-g-g-g-$

now see the dash . at the dashes boys can be placed fulfilling the requirement of the question.

so there are $3$ boys and $6$ places for boys to occupy.

it can be done in $6\cdot 54$ ways= $120$.

so total no of ways$=5!\cdot 120=120\cdot 120=14400$ ways