Adam and Maria decide to work on a project together but they need three other teammates to work with them. They want to

GMATinsight wrote: ↑

Wed Aug 26, 2020 3:56 am

Adam and Maria decide to work on a project together but they need three other teammates to work with them. They want to select atleast one teammate from Adam's 4 friends and at least 1 from Maria's 3 friends. In how many ways can they form the team to start working on the project as a team.

A) 12
B) 18
C) 28
D) 30
E) 32

Solution:

If two of the three teammates are Adam’s friends and one is Maria’s friend, then there are 4C2 x 3C1 = 6 x 3 = 18 ways to form the team.

If two of the three teammates are Maria’s friends and one is Adam’s friend, then there are 3C2 x 4C1 = 3 x 4 = 12 ways to form the team.

Therefore, there are a total of 18 + 12 = 30 ways to form the team.

Alternate Solution:

Without any restrictions, there are 7C3 = 7!/(3!*4!) = (7*6*5)/(3*2) = 35 ways to pick 3 people from a total of 3 + 4 = 7 people (Maria’s friends and Adam’s friends combined).

Of these 35 ways, 3C3 = 1 option consists only of Maria’s friends and 4C3 = 4 options consists only of Adam’s friends; hence neither of these options are allowable. Thus, the remaining 35 - (1 + 4) = 30 options contain at least one of Maria’s friends and one of Adam’s friends.

Answer: D