## anonymous 5 years ago 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.

1. anonymous

5 choose 3 divided by 21 choose 3

2. anonymous

so 3?

3. anonymous

is it 5/26?

4. anonymous

no

5. anonymous

6. anonymous

is it 3?

7. anonymous

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

8. anonymous

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

9. anonymous

5!/3(21-3)!

10. anonymous

Not quite

11. anonymous

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

12. anonymous

18-7

13. anonymous

no

14. anonymous

because when u do 21/3 it equals 7

15. anonymous

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

16. anonymous

no we don't use our calculators for it

17. 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$

18. anonymous

But that will make for a very long evening.

19. anonymous

can i butt in for a moment?

20. anonymous

it as 1/260

21. 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

22. 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.