Probability help

Dec 2009
61
0
In how many ways can 3 irishmen and 2 germans be chosen from 5 irishmen and 5 germans?
Hence find the probability that if 5 people are chosen a random from 5 irishmen and 5 germans, 3 of them will be irish.

I've done the first part and got 100 but i'm having trouble doing the second part, can someone help me please?
Thanks
 
Dec 2009
3,120
1,342
In how many ways can 3 irishmen and 2 germans be chosen from 5 irishmen and 5 germans?
Hence find the probability that if 5 people are chosen a random from 5 irishmen and 5 germans, 3 of them will be irish.

I've done the first part and got 100 but i'm having trouble doing the second part, can someone help me please?
Thanks
Hi Detanon,

there are 100 selections of 5 from the 10 containing 3 Irishmen.

there are \(\displaystyle \binom{10}{5}\) ways to choose 5 from 10

the selections containing 3 Irishmen and 2 Germans is a fraction of these,

therefore, the probability of a selection of 5 containing 3 Irishmen is \(\displaystyle \frac{100}{\binom{10}{5}}=\frac{100}{252}\)