Question

Find the value of ${}^6{C}_0{.}^{12}{C}_6{-}^6{C}_1{.}^{11}{C}_6{+}^6{C}_2{.}^{10}{C}_6{+}^6{C}_2{.}^{10}{C}_6{-}^6{C}_3{.}^9{C}_6{+}^6{C}_4{.}^8{C}_6{-}^6{C}_5{.}^7{C}_6{+}^6{C}_6{.}^6{C}_6$

Answer 1

${}^6{C}_0{.}^{12}{C}_6{-}^6{C}_1{.}^{11}{C}_6{+}^6{C}_2{.}^{10}{C}_6{+}^6{C}_2{.}^{10}{C}_6{-}^6{C}_3{.}^9{C}_6{+}^6{C}_4{.}^8{C}_6{-}^6{C}_5{.}^7{C}_6{+}^6{C}_6{.}^6{C}_6$

$1\times 924-6\times 462+15\times 210+15\times 210-20\times 84+15\times 28-6\times 7+1\times 1$

$924-2772+3150+3150-1680-420-41+1$

$2311$