A question paper is divided into three groups A, B and C which contain 4, 4 and 3 questions respectively. An examinee is required to answer 6 questions 2 from A, 2 from B, 1 from C and 1 from any group he/she likes. In how many ways can he/she afford to choose questions?

1. A question paper is divided into three groups A, B and C which
contain 4, 4 and 3 questions respectively. An examinee is
required to answer 6 questions 2 from A, 2 from B, 1 from C
and 1 from any group he/she likes. In how many ways can
he/she afford to choose questions?
Solution:
There are 3 cases
Case I 3 from A, 2 from B and 1 from C.
𝒄𝟑
𝟒
× 𝒄𝟐
𝟒
× 𝒄𝟏
𝟑
= 𝟕𝟐
Case II 2 from A, 3 from B and 1 from C.
𝒄𝟐
𝟒
× 𝒄𝟑
𝟒
× 𝒄𝟏
𝟑
= 𝟕𝟐
Case III 2 from A, 2 from B and 2 from C.
𝒄𝟐
𝟒
× 𝒄𝟐
𝟒
× 𝒄𝟐
𝟑
= 𝟏𝟎𝟖
Number of ways = Case I + Case II + Case III
𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐰𝐚𝐲𝐬 = 𝟕𝟐 + 𝟕𝟐 + 𝟏𝟎𝟖 = 𝟐𝟓𝟐