Hard? Perms and Combs Q (1 Viewer)

[mreditor16]

I'm just struggling to wrap my head around a solution for this question -

Ten male friends and six female friends go to the cinema and sit in a row. Everyone just sits at random. What is the probability that no two females are sitting next to each other?

All help will be appreciated!

 

[Drongoski]

Unlike braintic and InteGrand, I have a morbid fear of combinatorics. I find it hard to twist my brain this way and that way to see a solution.

But if the answer is something like 10! x ₁₁C₆ x 6!
I'll provide a solution.



Edit

I was providing the number of ways the 6 girls can sit without being adjacent.

So required probability = [10! x 11C6 x 6!]/16! = 10! x 11P6 / 16! as provided by InteGrand.

 

[InteGrand]

I'm just struggling to wrap my head around a solution for this question -

Ten male friends and six female friends go to the cinema and sit in a row. Everyone just sits at random. What is the probability that no two females are sitting next to each other?

All help will be appreciated!

We can use the 'insertion method'. Place the 10 males first (10! ways) and have 'gaps', i.e.

* M * M * M * ... * M *.

Each '*' represents a space between males, or on the sides. There are a total of 11 *'s.

We need 6 females to be placed into these gaps, with at most one female in each gap, which is done in 11P6 ways.

So the probability is ((10!)•(11P6))/(16!).

 

[porcupinetree]

 

[mreditor16]

Thanks heaps, guys! Got it now!!!

 

[braintic]

In general, with b boys and g girls, the probability is:

(b+1)C(g) / (b+g)C(g)

 

[kawaiipotato]

In general, with b boys and g girls, the probability is:

(b+1)C(g) / (b+g)C(g)

What is the reasoning for that?

 

[braintic]

What is the reasoning for that?

Didn't you delete the entire thread the last time I took the time to explain an answer?

 

[InteGrand]

Didn't you delete the entire thread the last time I took the time to explain an answer?

Even if he did, he can't this time since he wasn't the original poster.

 

[braintic]

Even if he did, he can't this time since he wasn't the original poster.

I realised that. But it still makes me disinclined to spend my time answering his question.

 

[InteGrand]

I realised that. But it still makes me disinclined to spend my time answering his question.

Maybe the mods can bring back those threads again and lock them (they brought them back before I think).

 

[braintic]

Maybe the mods can bring back those threads again and lock them (they brought them back before I think).

Once a thread or comment is deemed important enough to reinstate, the deleter should be warned not to delete it again (unless there are other mitigating circumstances such as identifying information or .......? ).

 

[sadpwner]

In general, with b boys and g girls, the probability is:

(b+1)C(g) / (b+g)C(g)

What type of questions could I apply this formula to? Is it only questions with this template where 2 girls don't sit together? Also, would you even get marks for just this lol.

 

[InteGrand]

What type of questions could I apply this formula to? Is it only questions with this template where 2 girls don't sit together? Also, would you even get marks for just this lol.

You would need to explain the reasoning, not just quote the formula (in other words, derive it).

 

[braintic]

I derived that as an example of something you could derive. It was not designed to be quoted.

 

[severus snake]

not really

 

[lukester64]

.