Permutation and Combination Calculator

Steps for Calculation

1. Input Values:
   • Total items (n): Enter the total number of items (e.g., 5).
   • Selected items (r): Enter the number of items to select (e.g., 3).
2. Calculate:
   • Click the Calculate button to compute the permutation and combination.
3. View Result:
   • The permutation (nPr) and combination (nCr) will be displayed below the button.

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Detailed Description

• Permutation (nPr):
  • A permutation is the number of ways to arrange r items from a set of n items where the order matters.
  • Formula: nPr=n!(n−r)!nPr=(n−r)!n!​.
  • Example: For n=5n=5 and r=3r=3, the permutation is 5!(5−3)!=1202=60(5−3)!5!​=2120​=60.
• Combination (nCr):
  • A combination is the number of ways to choose r items from a set of n items where the order does not matter.
  • Formula: nCr=n!r!⋅(n−r)!nCr=r!⋅(n−r)!n!​.
  • Example: For n=5n=5 and r=3r=3, the combination is 5!3!⋅(5−3)!=1206⋅2=103!⋅(5−3)!5!​=6⋅2120​=10.
• Factorial:
  • The factorial of a number nn (denoted as n!n!) is the product of all positive integers less than or equal to nn.
  • Example: 5!=5×4×3×2×1=1205!=5×4×3×2×1=120.

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Example Calculation

For n=5n=5 and r=3r=3:

• Permutation (nPr): 5!(5−3)!=1202=60(5−3)!5!​=2120​=60.
• Combination (nCr): 5!3!⋅(5−3)!=1206⋅2=103!⋅(5−3)!5!​=6⋅2120​=10.