Q11 of 31 Page 7

Find n if, C(n,7)=C(n,5).

Consider C(n,7) =C(n,5),


We know


So,



⇒ (n-5)!5! = (n-7)!7!




⇒ (n-5)(n-6)=42


⇒ n2 – 6n – 5n + 30 – 42 = 0


⇒ n2 – 11n – 12 = 0


⇒ n2 – 12n +n – 12 = 0


⇒ n(n-12) + 1(n-12)=0


⇒ (n+1)(n-12)=0


⇒ n = -1 , n =12


As number of terms cannot be negative,


So, n = 12.


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