Math Help: What is (n 0)=1?

  • Thread starter lalapnt
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In summary, the conversation was about binomial coefficients and their notation. The person was wondering about the notation \binom{n}{k} and how it relates to factorial notation. They were reassured that they have seen this concept before in combinatorics and that 0! is equal to 1.
  • #1
lalapnt
17
0
2cct0d5.png


in the above pic, (n 0) = 1?? what topic in math is that? i never saw this in my high school math and only saw it in my uni class. i don't know how that is. can someone please help me?
 
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  • #2
They are binomial coefficients. We define

[tex]\binom{n}{k}=\frac{n!}{k! (n-k)!}[/tex]

You have no doubt seen this before in combinatorics, but with other notation. It is a mystery to me why high school textbooks don't use the [itex]\binom{n}{k}[/itex] notation.

http://en.wikipedia.org/wiki/Binomial_coefficient
 
  • #3
super! and of course i know about binomial coefficients. just like this
cf53c9e57be2cdfe572da491e078d9ff.png


thank you very much. now I'm not scared anymore! :D
 
  • #5


I am not an expert in mathematics, but I can provide some insight on this topic. The notation (n 0) = 1 is commonly known as the "binomial coefficient" or "choose function" and is often used in combinatorics and probability. It represents the number of ways to choose a subset of n objects, where the order of the objects does not matter, and there are 0 objects in the chosen subset. This value is always equal to 1, as there is only one way to choose 0 objects from any set. This concept may not have been covered in your high school math class, but it is commonly taught in university-level math courses. I recommend consulting your professor or a math tutor for further clarification and practice with this topic.
 

1. What does (n 0)=1 mean?

(n 0)=1 is a mathematical notation used to represent the number of combinations of n objects taken 0 at a time. It is also known as the "empty set combination" and is equal to 1.

2. How is (n 0)=1 useful in math?

(n 0)=1 is useful in math when calculating the number of combinations of objects, especially when dealing with empty sets. It is also used in probability and statistics to calculate the number of ways an event can occur.

3. Can (n 0)=1 ever equal 0?

No, (n 0)=1 can never equal 0. This is because the number of combinations of n objects taken 0 at a time will always result in 1. This is a fundamental property of combinations.

4. How is (n 0)=1 related to other mathematical concepts?

(n 0)=1 is related to other mathematical concepts such as permutations, factorial, and binomial coefficients. It can also be used in the binomial theorem and in combinatorial identities.

5. Is (n 0)=1 the only combination that equals 1?

No, there are other combinations that can equal 1, such as (1 1)=1. However, (n 0)=1 is the only combination where n can be any non-negative integer and still result in 1.

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