Question:
If \(^n P_5 = 360360\), then \(^n C_5 = \)
If \(^n P_5 = 360360\), then \(^n C_5 = \)
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You don't need to find the value of \(n\). Just apply the relationship between \(P\) and \(C\) by dividing the permutation value by the factorial of the selection size.
Updated On: Jun 24, 2026
- 3030
- 3330
- 3300
- 3000
- 3003
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
There is a direct relationship between the number of permutations (\(^nP_r\)) and combinations (\(^nC_r\)) for the same \(n\) and \(r\).
Step 2: Key Formula or Approach:
The formula relating them is:
\[ ^nC_r = \frac{^nP_r}{r!} \]
Step 3: Detailed Explanation:
Given: \(^nP_5 = 360360\).
We need to find \(^nC_5\).
Using the formula for \(r = 5\):
\[ ^nC_5 = \frac{^nP_5}{5!} \]
We know that \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).
Substituting the values:
\[ ^nC_5 = \frac{360360}{120} \]
\[ ^nC_5 = \frac{36036}{12} \]
Divide by 12:
\[ 36036 \div 12 = 3003 \]
Step 4: Final Answer:
The value of \(^nC_5\) is 3003.
There is a direct relationship between the number of permutations (\(^nP_r\)) and combinations (\(^nC_r\)) for the same \(n\) and \(r\).
Step 2: Key Formula or Approach:
The formula relating them is:
\[ ^nC_r = \frac{^nP_r}{r!} \]
Step 3: Detailed Explanation:
Given: \(^nP_5 = 360360\).
We need to find \(^nC_5\).
Using the formula for \(r = 5\):
\[ ^nC_5 = \frac{^nP_5}{5!} \]
We know that \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).
Substituting the values:
\[ ^nC_5 = \frac{360360}{120} \]
\[ ^nC_5 = \frac{36036}{12} \]
Divide by 12:
\[ 36036 \div 12 = 3003 \]
Step 4: Final Answer:
The value of \(^nC_5\) is 3003.
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