Q9 of 31 Page 7

If nP4 = 12 nP2, then find the value of n.

nP4 : nP2= 12





⇒ (n-2)(n-3) = 12


⇒ n2 – 3n – 2n + 6 = 12


⇒ n2 – 5n + 6 – 12 = 0


⇒ n2 – 6n + n - 6 = 0


⇒ n(n-6) +1 (n-6)= 0


⇒ (n+1)(n-6)=0


⇒ n = -1 and n = 6


As the minimum value can be n = 4


So n = 6.


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