Find the value of `^6C_0 ^12C_6 - ^6C_1 ^11C_6 + ^6C_2 ^10C_6 - ^6C_3 ^9C_6 +^6C_4 ^8C_6 - ^6C_5 ^7C_6 +^6C_6 ^6C_6`

Find the value of quad ^(^^)6C_(0)^(12)C_(6)-^(6)C_(1)^(11)C_(6)+^(6)C_(2)^(10)C_(6)-^(6)C_(3)^(9)C_(6)+^(6)C_(4)^(8)C_(6)-^(6)C_(5)^(7)C_(6)+^(6)C_(6)^(6)C_(6)

Find the value of .^(6)C_(2)+.^(6)C_(3)+.^(7)C_(4)+.^(0)C_(5)+.^(9)C_(6) .

(^8C_0)/6-^8C_1+^8C_2xx6-^8C_3xx6^2++^8C_8 6^7

If (n-1) C_6 + (n-1)C_7 > nC_6 then

(""^8C_0)/6-""^8C_1+""^8C_2 .6-""^8C_3 .6^2+....+ ""^8C_8 .6^7 =

Give the empirical formula of the following . C_6H_12O_6 , C_6H_6 , CH_3COOH , C_6H_6Cl_6 .

The value of sum_(r=0)^(6) (""^(6)C_(r )*""^(6)C_(6-4)) is equal to: