Professors reign over tea

Probability Level 3

A "afternoon tea committee" will consist of 3 people, and is chosen out of 6 professors and 10 grad students. How many committee can there be, if at least one of the people on the committee must be a professor?

6 \times { 15 \choose 2 }

{ 16 \choose 3 } - {6 \choose 3 }

{ 6 \choose 1 } \times { 10 \choose 2 }

{ 16 \choose 3 } - { 10 \choose 3 }

1 solution

A Former Brilliant Member
Apr 1, 2015

Total number of ways to select 3 members from 16 persons (professor and grad students both) = ${16\choose3}$

Total number of ways in which 3 members can be chosen exclusively from students = ${10\choose3}$ .

As the given condition at least one member should be a professor the total number of ways are ${16\choose3}-{10\choose3}$

Amazing! I confused between the number of professors and grad students...but did the same way!

B.S.Bharath Sai Guhan - 6 years, 2 months ago

Yes, taking the complement makes this much easier, than trying to figure out how to force a professor in.

Chung Kevin - 6 years, 2 months ago

Professors reign over tea

1 solution

0 pending reports