Question

find n if 30 P (n,6)=P (n+2,7)

Answer 1

30P (n,6) = P (n+2,7)

30 n! / (n-6!) = (n+2)! / (n+2-7)!

30 n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)! / (n-6)! = (n+2)(n+1)n(n-1)(n-2)(n-3)(n-4)(n-5)! / (n-5)!

30 (n-5) = (n+2)(n+1)

30n - 150 = n^2 + n + 2n + 2

27n - 148 = n^2

n^2 - 27n + 148 = 0

NOW solve this quadratic equation u will get two values of n.



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