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.

Question

anonymous · Answer

5 choose 3 divided by 21 choose 3

anonymous · Answer

so 3?

anonymous · Answer

is it 5/26?

anonymous · Answer

no

anonymous · Answer

Satellite already gave you the answer.

anonymous · Answer

is it 3?

anonymous · Answer

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

anonymous · Answer

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 · Answer

5!/3(21-3)!

anonymous · Answer

Not quite

anonymous · Answer

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 · Answer

18-7

anonymous · Answer

no

anonymous · Answer

because when u do 21/3 it equals 7

anonymous · Answer

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

anonymous · Answer

no we don't use our calculators for it

anonymous · Answer

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 · Answer

But that will make for a very long evening.

anonymous · Answer

can i butt in for a moment?

anonymous · Answer

it as 1/260

anonymous · Answer

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 · Answer

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.