Discussion
4 members form a group out of total 8 members.
(i) In how many ways it is possible to make the group if two particular members must be included.
(ii) In how many ways it is possible to make the group if two particular members must not be included?
Answer: B
(i) Two particular members must be included. They take two of the four places, so two more come from the remaining six:
\[ {}^{6}C_{2} = 15 \]
(ii) Two particular members must not be included. All four come from the remaining six:
\[ {}^{6}C_{4} = 15 \]
The two answers coincide because \( {}^{6}C_{2} = {}^{6}C_{4} \) - choosing two to include is the same as choosing four to leave out.
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