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...
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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!

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

my third last line should have read....

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

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!

See response to:

math - bunni, Monday, June 1, 2009 at 12:26pm

ans. are correct

Sure! Let's go through each question one by one:

1. There are 13 horses running in a race. In how many different ways can the horses place first, second, or third?
To solve this problem, we need to find the number of permutations. Since the order matters (the first, second, and third positions are different), we'll use permutations. The formula for finding permutations is nPn = n!. In this case, we have 13 horses, and we need to find permutations of 3 horses (for the first, second, and third positions). Therefore, the number of different ways the horses can place is 13P3 = 13! / (13-3)! = 13! / 10! = 13 x 12 x 11 = 1,716 ways.

Your answer of 1,716 ways is correct.

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?
To solve this problem, we need to find the number of combinations since the order doesn't matter. The formula for finding combinations is nCk = n! / (k! * (n-k)!). In this case, we have 15 children, and we need to choose 5 children for the team. Therefore, the number of different 5-person teams that can be chosen is 15C5 = 15! / (5! * (15-5)!) = 15! / (5! * 10!) = 3003 ways.

Your answer of 3,003 ways is correct.

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?
To solve this problem, we need to find the number of permutations since the order matters. We have 26 letters in the alphabet, so there are 26 choices for the first letter, 25 choices for the second letter (since it can't be the same as the first), and 24 choices for the third letter (since it can't be the same as the first two). For the numbers, we have 10 choices for each number. Therefore, the total number of different license plates is 26x25x24x10x9 = 1,872,000.

Your answer for the number of possible license plates is incorrect. The correct answer is 1,872,000. This problem involves permutations since the order matters (the arrangement of the letters and numbers on the license plate).

Now let's move on to the questions about drawing letter tiles:

1. What is the probability that a randomly chosen letter will be a D?
To find the probability, we need to divide the number of favorable outcomes (the number of D tiles) by the total number of possible outcomes (the total number of tiles). In the word "INDEPENDENT", there are two D tiles. The total number of tiles is 11 because there are a total of 11 letters in the word. Therefore, the probability of choosing a D is 2/11.

Your answer of 2/11 is correct.

2. What are the odds in favor of a randomly chosen letter being an E?
To find the odds in favor, we need to divide the number of favorable outcomes (the number of E tiles) by the number of unfavorable outcomes (the total number of non-E tiles). In the word "INDEPENDENT", there are three E tiles. The number of non-E tiles is 11 (total number of tiles) - 3 (number of E tiles) = 8. Therefore, the odds in favor of choosing an E are 3:8.

3. What are the odds against a randomly chosen letter being a vowel?
To find the odds against, we need to divide the number of unfavorable outcomes (the number of non-vowel tiles) by the number of favorable outcomes (the number of vowel tiles). In the word "INDEPENDENT", there are four vowel tiles (I, E, E, and E), and the number of non-vowel tiles is 11 - 4 = 7. Therefore, the odds against choosing a vowel are 7:4.

I hope this explanation helps! Let me know if you have any more questions.