probability ..??

[maths_arghh234]

probability is really becoming my weak point .... here's the question i think you use combinations but i'm not sure .. .. that's where i need the help .. okay here's the question..
In a class of 20 pupils 10 are welsh 7 are english and 3 are scottish a sub-committee of 6 of three pupils is to be formed and it is to choose it's members at random from the 20 pupils
calculate the pprobability that the sub-committee contains a) no pupils b) 2 pupils of each nationality...

 

[galactus]

What do you mean a subcimmitte of '6 of three'?.

if I am understanding correctly, for part b, we have to choose two from each group.

So, we have \(\displaystyle \frac{\binom{10}{2}\cdot \binom{7}{2}\cdot \binom{3}{2}}{\binom{20}{6}}\)

Notice how the numbers in the top add up to the numbers in the bottom. We are choosing 6 from 20 altogether.

10+7+3=20 and 2+2+2=6

For part a, think about it. They are all pupils. So, how can we choose no pupils from the group?.

 

[maths_arghh234]

i'm not sure it's just what the question says :\

 

[galactus]

Oh, OK, they just mean a subcommittee of 6 formed from these 3 groups

 

[maths_arghh234]

ahh okay .. i just noticed the help you posted for part b) it didn't come up before .. yea i see it .... so is that combinations would i use the nCr button on my calculator ??

 

[galactus]

Yep. nCr is what a lot if calculators use.

 

[maths_arghh234]

kk thanks