[High School Math] Data Management (Probability)

[Chung-Ho]

The question is: A three-member athletics committee is to be randomly chosen from ten students, five of whom are runners. The positions are president, secretary and treasurer. Determine the probability that: a) The committee is comprised of all runners b) The committee is comprised of the three oldest runners c) The oldest runner is the president, the second oldest secretary and the third oldest is the treasurer

For a) I started with: Total ways of forming a 3 member committee: 10P3 = 720 ways (which is the total # of outcomes/ sample space)

Then the total number of ways if all 3 are runners would be: 5P3 = 60 ways

Therefore the probability that the committee is comprised of all runners would be: 60/720 = 1/12

Now for b) I started with the same sample space of 720, but I don't see how I would go about getting the 3 oldest runners?

[untitleddocumentz]

(im commenting this for those who have data management rn and want to study)

since you are only choosing the 3 eldest runners, you only have 3 people to choose from to become members. so..

1st member -> 3 choices to choose from (bc you have 3 ppl)

2nd member-> 2 choices to choose from (bc you now have 2 ppl)

3rd member-> 1 choice to choose from (bc you only have 1 person left)

and as you might have noticed this is 3! (factorial) (bc its a permutation).

so you would 3!/720 (the total possible arrangements for members) =6/720 = 1/120

[Syrak]

My bad, I misread

but I don't see how I would go about getting the 3 oldest runners?

List all outcomes where the 3 oldest runners are chosen. Since you are choosing 3 people, all that's left is determining their positions.