A) \[15!+16!\]
B) \[2(15!)(16!)(17!)\]
C) \[15!+16!+17!\]
D) \[16!+17!\]
E) \[2(15!+16!)\]
Correct Answer: B
Solution :
\[\left| \begin{matrix} 15! & 16! & 17! \\ 16! & 17! & 18! \\ 17! & 18! & 19! \\ \end{matrix} \right|\] \[=(15!)(16!)(17!)\left| \begin{matrix} 1 & 16 & 17.16 \\ 1 & 17 & 18.17 \\ 1 & 18 & 19.18 \\ \end{matrix} \right|\] \[=(15!)(16!)(17!)\left| \begin{matrix} 1 & 16 & 272 \\ 1 & 17 & 306 \\ 1 & 18 & 342 \\ \end{matrix} \right|\] \[=(15!)(16!)(17!)\left| \begin{matrix} 0 & 2 & 70 \\ 0 & 1 & 36 \\ 1 & 18 & 342 \\ \end{matrix} \right|\] \[=(15!)(16!)(17!)[1-(72-70)]\] \[=2(15!)(16!)(17!)\]
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