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In a high school, a committee has to be formed from a group of 6 boys M 1 , M 2 , M 3 , M 4 , M 5 , M 6 and 5 girls G 1 , G 2 , G 3 , G 4 , G 5 . (i) Let α 1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls. (ii) Let α 2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls. (iii) Let α 3 be the total numbers of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls. (iv) Let α 4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M 1 and G 1 are NOT in the committee together. List-I List-II (P) The value of α 1 is (1) 136 (Q) The value of α 2 is (2) 189 (R) The value of α 3 is (3) 192 (S) The value of α 4 is (4) 200 (5) 381 (6) 461 The correct option is :

1. (P) → (4); (Q) → (6); (R) → (2); (S) → (1)
2. (P) → (1); (Q) → (4); (R) → (2); (S) → (3)
3. (P) → (4); (Q) → (6); (R) → (5); (S) → (2)
4. (P) → (4); (Q) → (2); (R) → (3); (S) → (1)

Correct answer: (P) → (4); (Q) → (6); (R) → (5); (S) → (2)

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