2012 DSE Maths Paper 1 Q16

16.
(a)
In case of no restriction, 4 members are selected from 16 members (16C4).

If the 4 selected members are nominated by 4 different departments, 4 departments are firstly selected from the 8 departments (8C4),and then each department selects 1 member from the 2 nominated members (2⁴)

Pr(4 members nominated by 4 departments)
= 8C4 × 2⁴ / 16C4
= [8!/(4!4!)] × 2⁴ / [16!/(4!12!)]
= 8/13

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(b)
The 4 selected members can only be nominated by 2, 3 or 4 departments.

Pr(4 members nominated by at most 3 different departments)
= 1 - Pr(4 members nominated by 4 departments)
= 1 - (8/13)
= 5/13