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) at most 1 girl b) adam, anthony, and alice c) agnes and 2 other students

- anonymous

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- anonymous

no idea

- anonymous

hey INewton

- amistre64

we could always do this the long way :) and make a tree or chart

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## More answers

- amistre64

i havent been good yet at finding and filtering out all the redundnat possibilities :)

- anonymous

can u do it using permutations and combinations?

- amistre64

not yet, taking stats this summer...can you wait til august :)

- anonymous

ur taking ap stats?

- amistre64

college class...

- amistre64

im too old for ap i think

- anonymous

oh do u know the answers though???

- amistre64

not any anwers that i would trust; is there a multiple choice with this?

- anonymous

no

- amistre64

I know that with 3 positions avaiable; there are 10*9*8 possibilities; but how to remove the duplicates eludes me at the moment

- amistre64

we can always try to work with a similar situation; such as 2 spots to fill and 4 people; then see how to eliminate the duplicates

- anonymous

try it

- anonymous

The idea is that you try it.

- anonymous

(although admittedly it's not personally how I would do it - but I hate statistics anyway)

- amistre64

dividing the total by 2 worked in that case on paper; let me try another

- anonymous

?????

- amistre64

11 21 31 41
12 22 32 42
13 23 33 43
14 24 34 44

- amistre64

cross off all the duplicates

- amistre64

12
13 23
14 24 34

- amistre64

the total possible combination of 4 people and 2 spots is:
4*3/2

- amistre64

its the same for 5 people and 2 spots:
5*4/2

- amistre64

i wonder whatll happen with 3 spots...

- anonymous

??????

- amistre64

4 people and 3 spots has 4 possibilities

- amistre64

how we factorial that I dont know...

- amistre64

3C4 maybe.. let me find an online cal

- amistre64

the formula is:
people!
-----------------
spots!(people-spots)!

- amistre64

and thats the best i can do for you at the moment...

- amistre64

there seems to be 120 possible combonations; without repetition in all

- anonymous

wait, so what's c d and e??

- amistre64

4 boys can form an all boy team 4 times; so I would think that the rest are sure to have at least 1 girl; 116 out of 120 is sure to have at least 1 girl

- amistre64

c is agnus plus 2 other students; so we can take agnus out of the mix and have 2 spots to fill;
9!
------- = 36
2!(9-2)!

- amistre64

36 out of 120

- amistre64

what does it mean by positions? like captain, assistant, and runner? then we can have duplicates, just not the same person in all 3 spots and that changes things

- anonymous

d is 36/120???

- anonymous

????????

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