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If m satisfies the equation (m+5)Pₘ₊₁ = (11)/(2)(m-1)(m+3Pₘ), then the sum of the two values of m is
- 10
- 9
- 13
- 17
Correct answer: 13
Solution
Writing the permutations: (m+5)!/4! = (11/2)(m-1)(m+3)!/3!. Simplifying gives (m+4)(m+5)=11(m-1), i.e. m^2-2m-9... solving yields m=6 and m=7, whose sum is 13.
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