Question

In how many ways can six boys and five girls stand in a row if all the girls are to stand together but the boys cannot all stand together?

• A. $172,800$
• B. $432,000$
• C. $86,400$
• D. $Noneofthese$

Answer 1

The correct option is B $432,000$

6 boys & 5 girls

B B B B B B

$\to$ boys can be Arrange in = 6!

$\to$ girls seating position is $be{t}^n$ the boys so

boys can not come together = 5

$\to$ girls can arrange by these position = 5!

$\to$ total Arrangement = $6!\times 5!\times 5$

$=6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1\times 5$

$=4,32,000$