Thanks for helping!

Lauren

- Thread starter lp107
- Start date

Thanks for helping!

Lauren

There are 20 people in a class, 8 are men, 12 are women.

Four a chosen at random.

(a) What is the probability of getting just women?

(b) What is the probability of getting 1 man and 3 women?

\(\displaystyle \text{There are: }\;{20\choose4} \:=\:4845\text{ possible choices.}\)

\(\displaystyle \text{(a) There are: }\:{12\choose4} \:=\:495\text{ ways to choose 4 women.}\)

. . \(\displaystyle \text{Therefore: }\;P(\text{4 women}) \:=\:\frac{495}{4845} \;=\;\frac{33}{323}\)

\(\displaystyle \text{(b) There are: }\;{8\choose1} \:=\:8\text{ ways to choose 1 man.}\)

\(\displaystyle \text{There are: }\;{12\choose3} \:=\:220\text{ ways to choose 3 women.}\)

\(\displaystyle \text{Hence, there are: }\:8\times220 \:=\:1760\text{ ways to choose 1 man and 3 women.}\)

. . \(\displaystyle \text{Therefore: }\;P(\text{1 man, 3 women}) \;=\;\frac{1760}{4845} \;=\;\frac{352}{969}\)