Plz answer asap 4 matt and his wife have 20 good friends...

4. Matt and his wife have 20 good friends, twelve of them are male and eight of them are female. They decide to have a dinner party but can invite only eight guests. They decide to invite their guests by drawing their names from a hat. What is the probability that a) There will be an equal number of males and females at the dinner party? b) Mandie will be among those invited? c) There will be only one female guest? d) They will have only male guests? e) There will be at least one female guest?

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Transcript

00:01 Hello, so of part a, we want the probability that is going to be an equal number of males and females at the party.

00:08 So this is going to be equal to the number of ways to select four males from 12 males.

00:13 That's 12 choose four, and then times the number of ways to select four females from eight females.

00:19 So that's eight choose four.

00:21 So we have 12 choose four times eight choose four and then divided by the total number of ways to select eight names from 20 names.

00:28 So divided by 20 choose 8, and that's going to be equal to approximately 0 .2751.

00:40 So 27 .51 percent.

00:44 And then for part b, we have that the probability that mandy will be among those invited is going to be equal to the number of ways to select seven from the remaining 19 guys.

01:01 So that's going to be 19 choose 7.

01:06 So the numerator is going to be 19, choose 7.

01:09 And then we are going to be dividing by the number of weights to select 8 from 20.

01:18 So divided by 20 choose 8.

01:26 And that's going to give us approximately 0 .4 or 0 .40.

01:33 0, 0.

01:37 And then for part c, we want the probability.

01:44 There's only going to be one female guest.

01:46 So it's going to be 12 choose 7 times 8, choose 1...