# (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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