Probability

Question

Hey everyone.
If i had 4 boys and 8 girls. And i need to create 4 teams. Each team will be containing 2 girls and 1 boy.
What will be the number of variations of Team?
And what's the formula used?

And if i had If i had 4 boys and 6 girls. And i need to create 3 teams. Each team will be containing 2 girls and 1 boy.
What will be the number of variations of Team?
And what's the formula used?

thank you.

Answer 1

So you're talking about combination where order doesn't matter. 

I will be using the formula nCr=factorial n/factorial r * factorial(n-r)

Here you have 4 boys and 8 girls and you want to creat 4 different teams with a member of 2 girls and 1 boy.

First team:

you have 4 boys and 8 girls. So first team can be selected in 8C2*4C1=28*4=112

Second team:

Now you've 3 remaining boys and 6 remaining girls. so 2nd team can be selected in 6C2*3C1=15*3=45

3rd team:

2 remaining boys and 4 remaining girls. so 2C1*4C2=2*6=12

4th team:

1 remaining boys and 2 remainig girl=1

 

Please try the 2nd problem by yourself. good luck