A mathematical problem involving probability

This question is from a German high school maths course, which a mate's girlfriend is having trouble with...

You have 6 boys and 4 girls. You have to make two teams of 5 people. Each team must contain at least one girl. How many possible teams are there?

We have 3 different answers so far (240, 180, 170)... any one want to contribute more? Extra points if an explanation is included!

Cheers!

2!

Actually never mind...

I got 246 possibilities

EDIT - I think sGb27 is correct as I included teams with 4 girls which numbers 6.

In the way I studied probability:

Possible options:
4 boys, 1 Girl --> 6C4 x 4C1 = 15x4 = 60
3 boys, 2 Girls --> 6C3 x 4C2 = 20x6 = 120
2 boys, 3 Girls --> 6C2 x 4C3 = 15x4 = 60

Total - 240

I make it 240. Maybe not the simplest way, but this is how I figured it out:

Call them Team A and Team B.

There are 3 possibilities of how to group them:

1) Team A has one girl
2) Team A has two girls
3) Team A has three girls

For 1) and 3) there are 4 ways to arrange the girls, and for each arrangement of girls, 15 ways to arrange the guys (pick 4 guys from 6 to fill team A). For 2) there are 6 ways to arrange the girls between the teams, and for each one 20 ways to arrange the guys (pick 3 guys from 6 to fill team A). Add that all up and I make it 240.

Edit: oh hang on, if it doesn't matter which way round the teams are (ie Team A and Team B swapped count as the same thing) then I think it should be half, 120.

What I am wondering is, does it matter which girl / boy is in which group or are all boys and girls interchangeable with other boys / girls.
(That would make the number of possibilities a lot higher.)

Is everybody comfortable with their gender before the question is dealt with?

Mariposa, there are 10 distinct people. Call the boys:

Tom
Tim
James
John
Fred
Keydeck

and the girls:
Jenny
Sophie
Lisa
Helga

So a team containing Jenny, Tom, Tim, James and Fred is definitely different to a team with Keydeck, Sophie, Lisa, James and Tim

So it looks like 120 is winning the most votes... which makes the answer in the coursework wrong! They quote the answer as:

4C1 * 6C3 + 4C2 * 6C2 = 170

No one I know can work out how they come to this conclusion!

I don't want any part of this game, please remove me from the team roster.

And I'm not on speaking terms with Sophie at the moment so it would be inappropriate for us to be on the same team.

Ever since I found out that, according to quantun mechanics, there is a non-zero probability of me throwing a tennis ball through a wall, I gave up on studying probability.

An easier way to work it out: Choose 5 people for team A, 10C5 = 252. Remove 6 for the teams with no girls, and 6 for the teams with 4 girls, that leaves 240. Divide by 2 if ABCD1 vs 23456 is the same as 23456 vs ABCD1 (not clear from the question, but I assume so).

I think the mathematical correct way would be this formula (if you have to spell it out and not just put the result):



= 252 : 2 = 126 - 6 = 120.

I don't know how you would get a result of 170 either.

Helga's definitely a lesbian. I should know.

Hmm.. odd. I don't know why they seem to calculate only 4 people per team. Is it a "special" school with a "special" teacher?

As per most others, I get C(4,1)*C(6,4) + C(4,2)*C(6,3) + C(4,3)*C(6,2), but this equation, taken at face value, would mean you are only constructing one team, although that doesn't matter since you assume that the remaining students filter by default into the other team, and thus have no bearing.

Anyhoo, back to the pornsites.