Answer :

• 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

• 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=435 Ans: ³⁰C28=435

• 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=4060

Ans: ³⁰C27=4060