Put the must-have in first: If the group must include a particular person, put them in first.
Then you only choose the rest from the people who are left.
IB-style question — the captain must be in
A committee of 4 is chosen from 10 people. The team captain must be on the committee.
How many committees are possible?
Step by step
- Put the captain in — that uses 1 of the 4 places and 1 of the 10 people.
- Choose the other 3 from the remaining 9 people.
Final answer
84 committees.
The captain is fixed in (1 way); choose the other 3 from 9 → ⁹C₃ = 84.
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Just leave them out: If a particular person must be left out, simply choose from everyone else — that person isn't available.
IB-style question — the chair must NOT be in
A committee of 4 is chosen from 10 people. The chairperson must NOT be on this committee.
How many committees are possible?
Step by step
- Remove the chairperson — only 9 people are available.
- Choose all 4 from those 9.
Final answer
126 committees.