Hello, I'm doing some homework problems and I've gotten 17 of the 20 correct so far. There's just a few that I need help on, here is one of them.
A group of 9 males and 9 females volunteer for a medical study. Three volunteers are selected.
How many ways can the three subjects be selected from the 18 volunteers? (I found that this is 816 by doing C(18,3)
How many selections contain at least two females?
That's either all females or 2 females and 1 male
We can do this either of two ways.
Method 1.
From the 816 you already calculated we subtract
1. The number of selections of 3 males: 9C3 = 84
and
2. The number of selections with only one female and 2 males.
Choose her 9C1 = 9 ways and the two males 9C2 = 36 ways
That's 9*36 = 324 ways
3. Subtract from the 816 you calculated: 816-84-324 = 408 ways.
Method 2:
1. Those with 2 females and 1 male
Choose the 2 females 9C2 = 36 ways
Choose the 1 male 9C1 = 9 ways.
That's 36*9 = 324 ways
2. Those with 3 females.
Choose the 3 females 9C3 = 84
3. Total: 324+84 = 408 ways.
How many selections contain at most one female?
That's either all males or 2 males and 1 female.
Since there are an equal number of males and females,
that is, 9 males and 9 females, then this is the same
answer as the first one "either all females or 2 females
and 1 male"
Answer: 408
Edwin