Question

Aditya and Dhana sit for the selection of a six member team for a project X in company Z. If the team is to be split up into 2 three-person sub-teams, what percent of all the possible subteams that include Aditya also include Dhan?

• A. 10%
• B. 20%
• C. 30%
• D. 40%
• E. 50%

Answer 1

The correct option is D 40%

Option (d). Since we have fixed the selection of Aditya, the grouping of the remaining people into 2 groups containing 3 members each can be done in $\frac{5!}{(2!\times 3!)}$ ways =10 ways

Now, if both Aditya and Dhan are selected, 2 out of the three members in a sub-team are already selected. The third person can be anyone of the remaining 4, which means that we have 4 different possibilities. Thus, the percent of all possible subteams that include Aditya, also include Dhan = $\frac{4}{10}=40\%$