Probability help-Permutations?

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In summary, Pat caught n distinct fish from Lake Nebagamon last week but threw all of them back. Next week, Pat will catch k fish without throwing any back, and Lake Nebagamon will contain a total of f fish. Assuming random catching and no changes in the lake, the probability that exactly m of the fish caught next week are ones caught last week is 0.
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FTaylor244
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Last week, Pat caught n distinct fish from Lake Nebagamon, but threw all of them back at the end of the fishing trip. Next week, Pat will go fishing again at the same place, and this time will catch k fish without throwing any back. Lake Nebagmon will contain a total of f fish next week. Assuming that Pat catches fish at random, and that no fish die or are removed from the lake between last week and next week, find the probability that exactly m of the fish that Pat will catch next week are fish that Pat also caught last week.

I'm just wondering if I can solve this problem by using permutations and the counting principle, or if there's another advanced way of going about this that I'm not seeing at the moment. Thanks!
 
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  • #2
seems to me that the answer should be 0 as pat did not throw back the fishes he caught last week.
or if you want the probability that the fishes in 'm' are 'n' , please clarify it in your question.
 

1. What is the difference between permutations and combinations?

Permutations and combinations are both mathematical methods used to determine the number of possible outcomes in a given scenario. However, permutations take into account the order of the elements, while combinations do not. This means that in permutations, the order of the elements matters, while in combinations, it does not.

2. How do I calculate the number of permutations?

To calculate the number of permutations, you can use the formula nPr = n!/(n-r)!, where n is the total number of elements and r is the number of elements you are selecting. For example, if you have 5 letters and need to select 3 of them, the number of permutations would be 5P3 = 5!/(5-3)! = 5!/2! = 60.

3. What is the difference between permutations with repetition and without repetition?

Permutations with repetition occur when elements can be repeated in a sequence, while in permutations without repetition, each element can only be used once. For example, in the word "mississippi", there are 11 letters, but only 4 unique letters. Therefore, the number of permutations with repetition would be 11P4 = 11!/7! = 11*10*9*8 = 7920, while the number of permutations without repetition would be 11P4 = 11!/7! = 11*10*9*8 = 330.

4. How do I use permutations in real-life situations?

Permutations can be used in various real-life situations, such as determining the number of possible outcomes in a lottery or the number of possible seating arrangements at a dinner table. It can also be used in probability calculations, such as determining the likelihood of a certain event occurring.

5. What are some common mistakes to avoid when working with permutations?

One common mistake when working with permutations is forgetting to use the factorial (!) notation. Another mistake is confusing permutations with combinations, as they are similar but have different formulas and concepts. It is also important to make sure that the elements being selected or arranged are distinct and not repeated, as this can affect the outcome of the calculation.

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