math

1. There are 13 horses running in a race. In how many different ways can the horses place first, second, or third?
----> my answer: 1716 ways

2. There are 15 children on a basketball team. The coach needs to pick 5 children to start the game. How many different 5-person teams can be chosen?
----> my answer: 3003 ways

3. One state offers a zoo animal license plate that has 5 characters on it. The first three characters are letters and the last two are numbers. If each letter and number is used only once per plate, how many different license plates are possible? Is this a combination or permutation?
----> I coulsn't solve this one...
_______________________________

You randomly draw letter tiles from a bag containing the letters from the word INDEPENDENT.

1. What is the probability that a randomly chosen letter will be a D?
----> my answe: 2/11

2. What are the odds in favor of a randomly chosen letter being an E?

3. What are the odds against a randomly chosen letter being a vowel?
----> I couldn't do these [number 2+3]

I know these are lots of questions, but I really need some help. Can you please check my answers and explain the answers of those that I couldn't do? thanks a LOT!

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  1. All your given answers are correct

    For #3 at the top,

    the letters can be done in 26*25*24 ways.
    for the numbers I will assume that the zero can be in either of the two number positions, so 10*9

    no. of ways = 26*25*24*10*9 = ....

    for the last part the definition of odds is

    odds in favour of some event = prob(of that event to happen) / prob(of that event not to happen)
    often this will then be written as a ratio

    so #2, prob(E) = 3/11
    prob(not E) = 8/11
    so odds in favour of E being chosen = 3:11

    I am sure you can now do the last one
    I got 7:4

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  2. my third last line should have read....

    so odds in favour of E being chosen = 3:8

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  3. Thanks a lot!!!

    Now I only have two more questions left :) It goes together with the questions about the word INDEPENDENT. (You randomly draw letter tiles from a bag containing the letters from the word INDEPENDENT.)

    1. You randomly draw an N. Then, without replacing the first letter, you pick a D. Tell whether the events are independent or dependent. Then find the probability that both events occur.
    ---> I think it's a dependent event. But I'm having trouble solving for the probability.

    2. You randomly pick a T. You replace it. Then you pick an E. Find the probability that both events occur.

    These are my last questions :) THANKS. A LOT!

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  4. See response to:
    math - bunni, Monday, June 1, 2009 at 12:26pm

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  5. ans. are correct

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