Question:
If \( ^{11}P_r = 7920 \), then the value of \( r \) is equal to
If \( ^{11}P_r = 7920 \), then the value of \( r \) is equal to
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For permutation equations, try small values of \(r\) instead of expanding factorials fully.
Updated On: Apr 21, 2026
- \(7 \)
- \(6 \)
- \(5 \)
- \(4 \)
- \(3 \)
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The Correct Option is D
Solution and Explanation
Concept:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
Step 1: Apply formula.
\[ ^{11}P_r = \frac{11!}{(11-r)!} = 7920 \]
Step 2: Try suitable values.
\[ ^{11}P_4 = 11 \cdot 10 \cdot 9 \cdot 8 = 7920 \]
Step 3: Conclude.
\[ r = 4 \]
Step 1: Apply formula.
\[ ^{11}P_r = \frac{11!}{(11-r)!} = 7920 \]
Step 2: Try suitable values.
\[ ^{11}P_4 = 11 \cdot 10 \cdot 9 \cdot 8 = 7920 \]
Step 3: Conclude.
\[ r = 4 \]
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