Question

Out of a group of 3 females and 3 males, 3 people at radom enter a room. What is the probability that there are exactly 2 males in the room?



I know I have to use the combination formula. I did that and got 20. But the answer is 9/20. How do you get that?

Answer 1

exactly two males, so exactly one female
number of ways 3 people can be chosen out of 6 is \(\binom{6}{3}\) which you may have seen written as \(_6C_3\)
it is
\[\frac{6\times 5\times 4}{3\times 2}=20\] that is your denominator

Answer 2

you are choosing 2 out of the 3 males and one out of the 3 females
number of ways to choose 2 out of the 3 males is \(_3C_2=3\) and the number of ways to choose one out of the 3 females is \(_3C_1=3\)

Answer 3

number of ways to do this together is \(3\times 3=9\) which is why the answer is
\[\frac{9}{20}\]

Answer 4

thank you so much. I get it now!

Answer 5

wait, sorry. Why did you do 3C2=3?