Answer : (i) Given: ¹⁵C8 + ¹⁵C9 – ¹⁵C6 – ¹⁵C7

To prove: ¹⁵C8 + ¹⁵C9 – ¹⁵C6 – ¹⁵C7=0

We know that:

ⁿCr = ⁿCn-r

⇒15C8 + 15C9 – 15C6 – 15C7=15C8 + 15C9 – 15C9 – 15C8=0

Hence, proved that ¹⁵C8 + ¹⁵C9 – ¹⁵C6 – ¹⁵C7=0

(ii) We know that: ⁿCr + ⁿCr-1 = ⁿ⁺¹Cr

Therefore, n = 10 and r = 4

L.H.S = ¹⁰C4 + ¹⁰C3 = ¹¹C4

Hence, proved.