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Evaluate the combination:
9C2
Combination Definition:
A unique order or arrangement
Combination Formula:
| nCr= | n! |
| r!(n - r)! |
where n is the number of items
r is the unique arrangements.
Plug in n = 9 and r = 2
| 9C22 | 9! |
| 2!(9 - 2)! |
Factorial Formula:
n! = n * (n - 1) * (n - 2) * .... * 2 * 1
Calculate the numerator n!:
n! = 9!
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
9! = 362,880
Calculate (n - r)!:
(n - r)! = (9 - 2)!
(9 - 2)! = 7!
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
7! = 5,040
Calculate r!:
r! = 2!
2! = 2 x 1
2! = 2
Calculate 9C2
| 9C2= | 362,880 |
| 2 x 5,040 |
| 9C2= | 362,880 |
| 10,080 |
Excel or Google Sheets formula:
=COMBIN(9,2)
How does the Permutations and Combinations Calculator work?
Free Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = nPr
Number of combination(s) of n items arranged in r
ways = nCr including subsets of sets
This calculator has 2 inputs.
What 2 formulas are used for the Permutations and Combinations Calculator?
nPr=n!/r!
nCr=n!/r!(n-r)!
For more math formulas, check out our Formula Dossier
What 4 concepts are covered in the Permutations and Combinations Calculator?
- combination
- a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)! - factorial
- The product of an integer and all the integers below it
- permutation
- a way in which a set or number of things can be ordered or arranged.
nPr = n!/(n - r)! - permutations and combinations
Example calculations for the Permutations and Combinations Calculator
Permutations and Combinations Calculator Video
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I'm a mathematics expert with a deep understanding of combinatorics, specifically permutations and combinations. My expertise is backed by a comprehensive knowledge of the concepts involved, and I can confidently demonstrate the application of formulas and principles in solving problems.
Now, let's delve into the concepts mentioned in the article:
-
Combination (nCr):
- Definition: A unique order or arrangement.
- Formula: nCr = n! / (r! * (n - r)!)
- Factorial Formula: n! = n (n - 1) (n - 2) ... 2 * 1
-
Permutations (nPr):
- Definition: A way in which a set or number of things can be ordered or arranged.
- Formula: nPr = n! / (n - r)!
-
Factorial:
- Definition: The product of an integer and all the integers below it.
- Formula: n! = n (n - 1) (n - 2) ... 2 * 1
-
Permutations and Combinations Calculator:
- Calculates the following:
- Number of permutations (nPr) of n items arranged in r ways.
- Number of combinations (nCr) of n items arranged in r unique ways, including subsets of sets.
- Formulas used in the calculator:
- nPr = n! / r!
- nCr = n! / (r! * (n - r)!)
- Calculates the following:
-
Example Calculations for the Permutations and Combinations Calculator:
- 10 permutations of 6 (10P6)
- 5 combinations of 3 (5C3)
- 48 combinations of 26 (48C26)
- 210 permutations of 56 (210P56)
- 37 combinations of 4 (37C4)
- Subsets: How many subsets of at least 3 elements can be formed from a set of 4 elements?
-
Excel or Google Sheets Formula:
- Excel or Google Sheets formula for 9C2: =COMBIN(9,2), resulting in 36.
-
Permutations and Combinations Calculator Video Tags:
- The article mentions video tags related to combinations, factorials, permutations, and permutations and combinations.
In summary, the article covers essential concepts in combinatorics, providing formulas and practical examples. It also introduces a calculator that employs these formulas to calculate permutations and combinations, emphasizing their applications in various scenarios.
