A committee of 6 people is to be chosen from 9 women and 5 men. The 9 women and 5 men include a sister and brother. Find the number of ways in which the committee can be chosen if the sister and brother cannot both be on the committee. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_53 Year：2020 Question No：3(b)
Answer:
Total number of ways \(={ }^{14} \mathrm{C}_{6}(3003)\)
Number with sister and brother \(={ }^{12} \mathrm{C}_{4}(495)\)
Number required \(={ }^{14} \mathrm{C}_{6}-\)
\({ }^{12} \mathrm{C}_{4}=3003-495\)
2508
Alternative method for question 3(b)
Number of ways with neither \(={ }^{12} \mathrm{C}_{6}=924\)
Number of ways with either brother or sister (not both)
\(={ }^{12} \mathrm{C}_{5} \times 2(=792 \times 2)=1584\)
Number required \(=924+1584\)
\(=2508\)
Number with sister and brother \(={ }^{12} \mathrm{C}_{4}(495)\)
Number required \(={ }^{14} \mathrm{C}_{6}-\)
\({ }^{12} \mathrm{C}_{4}=3003-495\)
2508
Alternative method for question 3(b)
Number of ways with neither \(={ }^{12} \mathrm{C}_{6}=924\)
Number of ways with either brother or sister (not both)
\(={ }^{12} \mathrm{C}_{5} \times 2(=792 \times 2)=1584\)
Number required \(=924+1584\)
\(=2508\)
Knowledge points:
5.2.1 understand the terms permutation and combination, and solve simple problems involving selections
Solution:
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