Probability of girls sit together/ separated

[desmond iking]

Homework Statement

Ten Students sit in a row. Find the probability of 6 boys and 4 girls can be arranged if (i) all girls are side by side?
(ii) all girls are separated by boys

Homework Equations

The Attempt at a Solution

my working for part i is 4!x7!=120960

for part ii, why can't i just take 10! -120960=3507840 ? the ans given is 604800

 

[Fredrik]

Part (i) looks OK to me. (7 possible positions for the first girl, 6! ways to order the boys in the remaining positions). If you take 10! minus the result of part (i), what you find is just the number of ways to not have four girls in a row. This includes e.g. gggbgbbbbb which has three girls next to each other, but the problem is asking for arrangements like gbgbbgbgbb, where no two girls are next to each other.

 

[HallsofIvy]

Your question "Find the probability of 6 boys and 4 girls can be arranged" doesn't really make sense. From what you do, it appears that the question was really "Find the number of different ways 6 boys and 4 girls can be arranged".