There are ten female board members and twenty male board...

There are ten female board members and twenty male board members. How many ways are there to make a committee of twelve board members? __ways How many ways are there to make a committee of twelve board members if exactly two must be female? ___ways Determine the probability of selecting a committee of twelve board members where exactly two of the members were female. Write your answer as a decimal, rounded to the nearest thousandth. Answer:

Transcript

00:01 All right, in your question, you're told we have 10 female board members and 20 male board members, and we're looking to form a committee using 12 board members.

00:09 Okay, what this is actually referring to is what's called a combination.

00:14 This is the symbol you typically see for a combination where we have a certain population, n, that we're trying to select number of groups of a certain size out of.

00:28 The formula for this is given by n factorial over r factorial times n minus r factorial.

00:42 Now, this is a typical scientific calculator program that's available, so i'm not going to go through the formula, but if you needed the formula, you could use it for that.

00:53 Okay, so what i'm going to be typing in my calculator here for part a would be we have 30 people to choose from, and we want to figure out.

01:02 How many different possible groups of 12 there are.

01:05 Because we don't care in this part a question of whether it's groups of male, certain number of male and females here.

01:13 So just straightforward, 30 ncr 12 is going to be 86 ,493 ,225.

01:29 Okay, moving on to the next question, how many of those groups would have exactly two females and 10 males.

01:37 This gets a little bit more complicated here because we're going to select, let's go after the two females first.

01:46 We only have 10 females to choose from and we want to figure out how many different groups of two there would be.

01:53 And then we want to multiply that to how many groups of 10 males there would be.

02:01 So i'm going to say there are 20 males to choose from and we want groups of 10 from them.

02:11 Okay, so let me take a second here to do that on the calculator...

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