Question

14 In how any ways can 7 boys and 5 girls be arranged
in a row so that no two girls come together?
​

Answer 1

Answer:

33868800

Step-by-step explanation:

If we position the boys first, there are then 8 positions where girls can be places --- 6 between boys and 1 at each end.  So...

# ways of doing this

= ( # ways of arranging the 7 boys ) × ( # ways of selecting 5 places from the 8 positions to put girls in ) × ( # ways of arranging the girls in those places )

$\displaystyle =7! \times \binom85\times 5!\\\\=\frac{7!\times 8!\times 5!}{5!\times 3!}\\\\=\frac{7!\times 8!}{3!}\\\\=7\times6\times5\times4\times3\times2\times8\times7\times6\times5\times4\\\\=33868800$