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.