Selection with family/relationship restrictions

Select a group where certain individuals have special relationships (siblings, twins, couples) and restrictions apply to whether they can both be included or excluded together.

3 questions · Moderate -0.1

5.01a Permutations and combinations: evaluate probabilities
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CAIE S1 2022 June Q2
6 marks Moderate -0.3
2 There are 6 men and 8 women in a Book Club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
  1. In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?
  2. In how many different ways can the committee be selected if Mrs Lan must be on the committee and there must be more women than men on the committee?
CAIE S1 2020 November Q3
6 marks Standard +0.3
3 A committee of 6 people is to be chosen from 9 women and 5 men.
  1. Find the number of ways in which the 6 people can be chosen if there must be more women than men on the committee.
    The 9 women and 5 men include a sister and brother.
  2. Find the number of ways in which the committee can be chosen if the sister and brother cannot both be on the committee.
CAIE S1 2016 November Q1
3 marks Moderate -0.3
1 A committee of 5 people is to be chosen from 4 men and 6 women. William is one of the 4 men and Mary is one of the 6 women. Find the number of different committees that can be chosen if William and Mary refuse to be on the committee together.