Required person / fixed member
Practice Flashcards
Flip to reveal answersHow do you count groups that MUST include a particular person?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Required person / fixed member
Sign up free to track progress and get spaced-repetition review schedules.
Question
How do you count groups that MUST include a particular person?
Answer
Put that person in first (they use one place), then choose the rest from the people who are left.
Question
'A committee of 4 from 10 must include the captain' — how many?
Answer
Captain in, choose 3 from the remaining 9: ⁹C₃ = 84.
Question
How do you count groups that must NOT include a particular person?
Answer
That person is unavailable, so just choose from everyone else.
Question
'A committee of 4 from 10 must exclude one person' — how many?
Answer
Choose all 4 from the other 9: ⁹C₄ = 126.
Question
After fixing or removing a required/forbidden person, what's left to do?
Answer
An ordinary selection (ⁿCᵣ) on the remaining people for the remaining places.
Question
When you 'include' a fixed member, how do the numbers change?
Answer
Both drop by 1: one fewer place to fill AND one fewer person to choose from.
Question
When you 'exclude' a person, how do the numbers change?
Answer
The number of people drops by 1, but the number of places stays the same.
Question
Trigger words for a 'required person' question?
Answer
'must include', 'always plays', 'the chair is on the committee', or 'must not be chosen / refuses'.
Read the notes
Full study notes for Required person / fixed member
Topic 1.10 hub
Counting & binomial (HL only)
More from Topic 1.10
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free