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Incompatible analysts

CombinatoricsMedium

A team of $4$ is chosen from $8$ analysts. Analysts Ann and Bob refuse to serve together on the same team. How many valid teams exist?

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Hint

Subtract the teams containing both of them from all teams.

Solution

All teams: $(4 8) = 70$ .
Teams containing both Ann and Bob need $2$ more members from the other $6$ : $(2 6) = 15$ .
Valid teams are all teams minus those: $70 - 15$ .
Therefore the answer is $55$ .

Answer: $55$