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Question with Counting.

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A PE class has 12 students, 6 girls and 6 boys. The coach has 4 jerseys in each of 3 colors to mark 3 teams for a soccer tournament. If the coach wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys? (Jerseys of the same color are indistinguishable.)

May 4, 2021

#1
+311
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NVM I found 2 ways to do it(My dad helped me, we talked about it all through supper.)

The way I used was just countnig, not cpunting the opisite and then subtracting.

Boys:

1.) 3 2 1   = 360

2.) 2 2 2   = 90

Girls:

1.) 1 2 3   = 60

2.) 2 2 2   = 90

(Each number is how many people in each group, and then I used combinintry.)

360 x 60 + 90 x 90 = 29700 ways!

The other way is solving they ways that DON'T work. I'm not going to explain it but I can put a screenshot of their explantion.

- WillBill

May 4, 2021
edited by WillBillDillPickle  May 4, 2021
#2
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BBG BBG BGG BGG is our only way of splitting it up.

To make our groups, 6!*6!/2/2/2/2, but since some groups are the same, 6!*6!/2/2/2/2/2/2 = 8100.

8100 ways of making groups, 4*3*2 of giving colours.

8100*4*3*2 = 194400

Edit:

I read the question wrong, it's 3 groups of 4, not 4 groups of 3.

=^._.^=

May 4, 2021
edited by catmg  May 4, 2021
#3
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Not corect though, but intreasting method.

WillBillDillPickle  May 4, 2021
#4
+1940
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I read the question wrong, going to retry. :((

=^._.^=

catmg  May 4, 2021