An Information Technology Specialist is researching eight new computer programs for her team to use. The programs are labeled $1,2,3,4,5,6,7,$ and $8.$ In order to maintain compatibility with their current software, the following rules apply:

Programs $1$ and $8$ cannot be used together.

Programs $2$ and $3$ must be used together.

Programs $4$ and $7$ must be used together.

Programs $5$ and $6$ cannot be used together.

Based on the above information, which of the following groups of programs could be used by the team?