Question

11\( (10P_7) \) =

• A. \( 11P_7 \)
• B. \( 10P_8 \)
• C. \( 11P_8 \)
• D. \( 11P_9 \)
• E. \( 10P_9 \)

Hint:

For permutation problems involving multiplication of factorials, simplify the expressions and ensure correct interpretation of the formula for permutations.

Answer 1

The Correct Option is C

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 \( 11P_8 \).