Combination of Non Adjacent Numbers

In summary, a combination of non adjacent numbers involves selecting a group of numbers from a larger set where the selected numbers are not next to each other. It is important in various fields such as statistics, probability, and computer science for solving problems without restrictions on the positions of elements. The number of possible combinations depends on the size of the set and can be calculated using the binomial coefficient formula. A combination differs from a permutation in that it focuses on selection rather than arrangement. This concept has practical applications in creating unique passwords, optimizing investments, designing schedules, and data analysis in various industries.
  • #1
SamitC
36
0
Suppose there are numbers 1, 2, 3, 4, 5, 6, 7, 8. Question is: How many ways can we pick 4 non adjacent numbers (order does not matter)?
Now, as per formula it is C(n-r+1,r) = C(8-4+1,4) = C(5,4)=5.
Crosschecking, I could find only four: 1,3,5,7 : 1,3,5,8 : 1,4,6,8 : 2,4,6,8
Not sure which 5th one I am missing?
 
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  • #3
Thanks.
 

FAQ: Combination of Non Adjacent Numbers

What is a "Combination of Non Adjacent Numbers"?

A combination of non adjacent numbers is a mathematical expression that involves selecting a group of numbers from a larger set of numbers, where the selected numbers are not next to each other in the set.

What is the purpose of studying "Combination of Non Adjacent Numbers"?

The study of combination of non adjacent numbers is important in various fields such as statistics, probability, and computer science. It helps in analyzing and solving problems that involve selecting elements from a set without any restrictions on their positions.

How many combinations of non adjacent numbers can be formed from a set of numbers?

The number of combinations of non adjacent numbers that can be formed from a set of numbers depends on the size of the set. For a set of n numbers, there are (2^n - n) possible combinations. This can be calculated using the binomial coefficient formula, nCr = n! / (r!(n-r)!), where r represents the number of elements in the combination.

What is the difference between a combination of non adjacent numbers and a permutation of non adjacent numbers?

A combination of non adjacent numbers is a selection of elements from a set without any specific order or arrangement, while a permutation of non adjacent numbers is a specific arrangement of elements from a set. In other words, a combination focuses on the selection of elements, while a permutation focuses on the arrangement of elements.

How can "Combination of Non Adjacent Numbers" be applied in real life?

Combination of non adjacent numbers has various real-life applications, such as in creating unique passwords or codes, optimizing investments in a portfolio, and designing efficient schedules for tasks or events. It can also be used in data analysis and decision-making processes in fields such as marketing, finance, and sports.

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