Question:
11\( (10P_7) \) =
11\( (10P_7) \) =
Show Hint
For permutation problems involving multiplication of factorials, simplify the expressions and ensure correct interpretation of the formula for permutations.
Updated On: Apr 7, 2026
- \( 11P_7 \)
- \( 10P_8 \)
- \( 11P_8 \)
- \( 11P_9 \)
- \( 10P_9 \)
Show Solution
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The Correct Option is C
Solution and Explanation
The formula for the number of permutations of \(r\) objects taken from a set of \(n\) objects is given by:
\[
nP_r = \frac{n!}{(n-r)!}
\]
In the given question, \( 11 \) represents the total number of objects, and \( 7 \) represents the number of objects chosen. So:
\[
11 \times (10P_7) = 11 \times \frac{10!}{(10-7)!} = 11 \times \frac{10!}{3!}
\]
This is equivalent to:
\[
11P_8 = \frac{11!}{(11-8)!}
\]
Thus, the correct answer is \( 11P_8 \).
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