(i) If nC7 = nC5, find n.

(ii) If nC14 = nC16, find nC28.


(iii) If nC16 = nC14, find nC27.


(i) Given: nC7 = nC5


To find:n=?


We know that:


nCr = nCn-r


⇒ nC7= nCn-7


⇒ nCn-7= nC5


⇒n-7=5


⇒n=7+5=12


Ans:n=12


(ii) Given: nC14 = nC16


To find: nC28=?


We know that:


nCr = nCn-r


⇒ nC14= nCn-14


⇒ nCn-14= nC16


⇒n-14=16


⇒n=16+14=30


⇒n=30


So,


nC28= 30C28


⇒30C28=


⇒30C28=


⇒30C28=


⇒30C28=


⇒30C28=


⇒30C28=435


Ans: 30C28=435


(iii) Given: nC16 = nC14


To find: nC27=?


We know that:


nCr = nCn-r


⇒ nC14= nCn-14


⇒ nCn-14= nC16


⇒n-14=16


⇒n=16+14=30


⇒n=30


So,


nC27= 30C27


⇒30C27=


⇒30C27=


⇒30C27=


⇒30C27=


⇒30C27=


⇒30C27=4060


Ans: 30C27=4060


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