Ten students are applying for 3 positions on a team. the students include 4 boys (adam, alex, anthony, and arnold) and 6 girls (abbey, aurora, agnes, alice, amanda, and anna). all the students have an equal chance of being selected. find the probability that the students selected will include: a) adam, anthony, and alice b) agnes and 2 other students

- anonymous

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- anonymous

ok

- anonymous

adam anthony and alice, thats 3 people
so favorable is 3. and total is 10 choose 3 , correct ?

- anonymous

so 3 / 10 choose 3

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## More answers

- anonymous

3 / ( 10 choose 3) , remember 10 choose 3 is total ways of choosing 3 people out of ten , order does not count

- anonymous

that's it?

- anonymous

and 3 cuz you have 3 favorable, they specified

- anonymous

yeah, its easy :0

- anonymous

well that one anyway

- anonymous

brb

- anonymous

wait so answer is????

- anonymous

.025

- anonymous

fraction form?

- anonymous

3 / ( 120

- anonymous

1/40

- anonymous

wait, why does it matter?

- anonymous

probability is usually in fraction form

- anonymous

if youre doing this online, let me know if its correct

- anonymous

it can be a decimal between 0 and 1

- anonymous

ok

- anonymous

B now

- anonymous

wait, is it right ?

- anonymous

I'm not sure? going over it on monday

- anonymous

in class

- anonymous

let's do B

- anonymous

Lol

- anonymous

ok agnes, thats 1

- anonymous

2 other students? well there are 9 students left, and you choose 2

- anonymous

so 1 + 9 choose 2 , thats the favorable , and the denominator is again , the same

- anonymous

newton, do you concur?

- anonymous

( 1 + 9 C 2 ) / ( 10 C 3 )

- anonymous

oh newton is gone, darn

- anonymous

why did u add 1??

- anonymous

Oh by the way, if the answer to the first one is 1/40, and there are 10 * 9 * 8 ways of choosing the first 3 people, that implies that 18 teams will have those three in any order (they don't)

- anonymous

1 for agnes, since they told you , you must choose her

- anonymous

It makes more sense just to say there are 10C3 ways of picking the 3 students (nCr takes into account the ordering problem) and one of these will be the 3 we want - so it is simply 1/10C3, not 3/10C3

- anonymous

what??? I'm confused. what's the setup

- anonymous

i get 37/120 , unless i did something wrong

- anonymous

or should it be multiplied, hmmm

- anonymous

ohhh

- anonymous

sorry it is ( 1 * 9 choose 2 ) / 10 choose 3

- anonymous

since there is 1 way to choose agnes, then there is 2 you have to choose among the 9 left

- anonymous

so 36/ 120 = 3/ 10

- anonymous

ah I see lol, but I still don't understand this permutation and combination stuff? is there a way that u can explain to me?

- anonymous

permutations is where order counts, combination is where order does not count

- anonymous

thats the "big" difference

- anonymous

how do u know what numbers to put for the probability

- anonymous

like 9C2/10C3

- anonymous

I don't get how u set up the numbers in order to find the probability

- anonymous

well we use multiplication rule

- anonymous

there are how many ways to choose agnes, one way.
and for each of that way we can choose from whats left (9 people) 2 people we can choose. so we multiply these .

- anonymous

if you can do step one in k ways, and for each of those ways you can do step m, then there are a total of k * m ways

- anonymous

so we did ( 1 * 9C2) , thats the favorable

- anonymous

what grade r u in btw

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