How many teams?

Probability Level 3

The math team is putting together a 2-person team for a certain competition. 8 members can only do Algebra, 5 members can only do Geometry, and 2 members can do both. If the team must include one person doing Algebra and one person doing Geometry, how many different teams can be formed?


The answer is 67.

Amogha Pokkulandra by Amogha Pokkulandra , 23, USA

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1 solution

First consider having an only-Algebra person and an only-Geometry person team. That would be 8 x 5 = 40 .

The second case is having an Alg-Geo person with an only-Algebra person. That would be 2 x 8 = 16 .

Next have an Alg-Geo person with an only-Geometry person. That would be 2 x 5 = 10 .

Now take two Alg-Geo people. Since it is a two-person team, there is only 1 way.

40 + 16 + 10 + 1 = 67 \boxed{67} .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

OR You can do this

( 15 2 ) − ( 8 2 ) − ( 5 2 ) = 67 \binom{15}{2}-\binom{8}{2} - \binom{5}{2}=67

Kushal Bose - 4 years, 2 months ago

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