Combanatorics Problem (Probability Application)

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In summary, the conversation revolved around determining the probabilities of two tape recorders being shipped to L.A. out of a load of 50, and the probability of one going to L.A. and the other to Miami. The equations used were (35 choose 2)/(50 choose 2) and [(35 choose 1)(15 choose 1)]/(50 choose 2), resulting in probabilities of 0.4857 and 0.4286 respectively.
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Shoney45
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Homework Statement

From a load of 50 Panasonic tape recorders 35 are destined for L.A. and 15 are destined fro Miami. If two are shipped to Trenton by mistake and the "selection" is made at random, determine the probabilities that:

a) both should have gone to L.A.

b) one should have gone to L.A. and the other to Miami



Homework Equations





The Attempt at a Solution

Alright, I think I'm starting to get the hang of these. But I want to bounce this one off of somebody to get a second set of eyes on it.

For P(both to L.A.) I am getting (35 choose 2)/(50 choose 2) = 0.4857

For P(one to each city) I am getting [(35 choose 1)(15 choose 1)]/(50 choose 2) = 0.4286
 
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Looks good to me
 

1. What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects in a systematic way. It involves the study of discrete structures and their properties, and is often used to solve problems related to probability and statistics.

2. What is a combinatorics problem?

A combinatorics problem is a mathematical problem that involves counting or arranging objects in a specific way. It can also refer to a problem that involves making choices or selecting items from a given set.

3. How is combinatorics used in probability?

Combinatorics is used in probability to calculate the number of possible outcomes in a given scenario. It helps in determining the likelihood of certain events occurring and is essential in solving problems related to probability and statistics.

4. What are some common applications of combinatorics?

Combinatorics has many practical applications, including in computer science, genetics, cryptography, and game theory. It is also used in various industries, such as finance, marketing, and logistics, to solve problems related to decision making and optimization.

5. How can I improve my skills in solving combinatorics problems?

To improve your skills in solving combinatorics problems, it is important to have a strong foundation in basic mathematical concepts, such as permutations, combinations, and probability. Practice regularly and try to solve a variety of problems to gain a better understanding of the subject. Additionally, reading textbooks and attending lectures or workshops can also help improve your skills in combinatorics.

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