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Educational Fellowship A university received 9 applications for three postdoctorate fellowships. Five of the applicants are men and four are women. Find these probabilities.$$\begin{array}{l}{\text { a. All } 3 \text { who are selected are men. }} \\ {\text { b. All } 3 \text { who are selected are women. }} \\ {\text { c. Two men and one woman are selected. }} \\ {\text { d. Two women and one man are selected. }}\end{array}$$

a.$\dfrac{5}{42}$b.$\dfrac{1}{21}$c.$\dfrac{10}{21}$d.$\dfrac{5}{14}$

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 5

Sampling and Data

Probability Topics

University of North Carolina at Chapel Hill

Piedmont College

Oregon State University

Lectures

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05:48

Job Applications Ten peopl…

01:34

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So in this problem we have five men and for women, Onda, we want toe randomly select three people Thio give them fellowships and we want to know the probability of the falling for situations. So let's look at part A, um we want to know that all three fellowships the probability of all three fellowships go to men. Um, so those probability actually equals, um, the number of choices. We could have to select three people from five men, so the numerator would be five shoes three divided by the total number of choices. We could have to select three out of nine people. So the denominator would be nine shoes three. And the final result would be 0.11 night. Okay. And the next part we want to know all three. The probability of all three fellowships. Goto women. Um, similarly, the new murder should be the number of choices we could have Thio select three women out of four, so it should be four. Choose three and the same as above. Divided by 9 to 3. And the result goes to why no. 48 So the next part is a little bit different because we want toe first, select two men out of five, then select one woman out of four. So I have We're going to do this and two step two steps. The first one should be five choose to times for choose one. So these are the the number of choices we could have to select two men out of five and then one woman out of four and divided by nine. Choose three. This is 10 times four. Divided by 84 Goes to point or 76 Okay. And finally, the last part. This is similar, um, with part C. First, we want to select two when women out of four, which should be for Jews to And then so that you are men out of five, which is five choose one divided by nine shoes. Three It goes to six times I've reminded by 84 and finally the result is point 357 and we're done

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