A table has 4 boys and 4 girls sitting around it. If the sitting is arranged at random find the probability that all boys sit together

Question

callisto · Answer

Can you find the number of arrangements when all boys sit together?

anonymous · Answer

it would be 4!*5!

callisto · Answer

Right. What about the total number of arrangements of 8 people?

anonymous · Answer

its 7! because its (n-1)!?

callisto · Answer

No?! There are 8 people you have to arrange in order.
So, for the first place, you can have 8 choices.
For the second place, you can have 7 choices.
For the third place, you can have 6 choices.
.
.
. 
Then the total number of arrangement is...?

anonymous · Answer

8! ?

callisto · Answer

Yes.
So, the probability required is the expected outcome (number of arrangements of 4 boys sitting together) / total number of arrangements.

anonymous · Answer

so it is 4!/8!?

callisto · Answer

No.

callisto · Answer

What is the expected outcome?

anonymous · Answer

there are 4! ways (for the boys to sit together) and there are 5! all together so 4!*5!?

callisto · Answer

Yes. Then, divide it by the total number of arrangements of 8 people.