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- anonymous

assume that a perfessional baseball team has 11 ptchers,5 infielders, and 10 other players. if 3 players names are selected at random, determine the probl that all 3 are infielders.

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- anonymous

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- anonymous

5 choose 3 divided by 21 choose 3

- anonymous

so 3?

- anonymous

is it 5/26?

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- anonymous

no

- anonymous

Satellite already gave you the answer.

- anonymous

is it 3?

- anonymous

whats does 5 choose 3 devided by 21 choose 3 mean its only suppose to be 1 number rite

- anonymous

Choose is the name we sometimes give to the binomial coefficient function:
\[\text{n choose k} = {n\choose k} = \frac{n!}{k!(n-k)!}\]

- anonymous

5!/3(21-3)!

- anonymous

Not quite

- anonymous

5 choose 3 = \(\frac{5!}{3!(5-3)!}\)
21 choose 3 = \(\frac{21!}{3!(21-3)!}\)
Then divide those two values to find
\[\frac{\text{5 choose 3}}{\text{21 choose 3}}\]

- anonymous

18-7

- anonymous

no

- anonymous

because when u do 21/3 it equals 7

- anonymous

Are you being taught to do this on your calculator using the Cr function?

- anonymous

no we don't use our calculators for it

- anonymous

Doing it by hand you have \[\frac{21!}{3!*18!} = \frac{21*20*19*18!}{3! * 18!} = \frac{21*20*19}{3*2} \]\[= 7*10*19 = 70*19 = 700 + 630= 1330\]

- anonymous

But that will make for a very long evening.

- anonymous

can i butt in for a moment?

- anonymous

it as 1/260

- anonymous

If i want to know the number of ways to choose 3 people (items, whatever) out of a set of 21 I reason as follows: there are 21 choices for the first person, 20 for the next and then 19 for the last. by the counting principle there are then 21*20*19 ways to do this. But this counts (a,b,c) differently than (b,c,a) for example so I have over-counted by the number of ways I can permute 3 things. There are 3*2 = 6 such permutations. Thus the number of ways to choose 3 from a set of 21 is 21*20*19/3*2.
Similarly the number of ways to choose 3 from a set of 5 is 5*4*3/3*2 and the number of ways to choose 4 out of 11 is 11*10*9*8/4*3*2
etc

- anonymous

Hello,
Your chance of picking one is 5/26, then, once you've picked him, there are only 4 left out of 25 and once you've picked that player, there's only 3 left out of 24 to choose from (like in elementary school picking teams) giving you:
(5/26)*(4/25)*(3/24) = 1/260, like you said.

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