Sixteen players \( {S}_{1},{S}_{2}, {S}_{3}\dots {S}_{16}\) play in a tournament. Number of ways in which they can be grouped into eight pairs so that \( {S}_{1}\) and \( {S}_{2}\) are in different groups, is equal to
( )
A. \( \frac{\left(14\right)!}{{2}^{6}\times\;6!} \)
B. \( \frac{\left(15\right)!}{{2}^{7}\times\;7!}\)
C. \( \frac{\left(14\right)!}{{2}^{7}\times\;6!}\)
D. \( \frac{\left(14\right)!}{{2}^{6}\times\;7!}\)