In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5.
(i) Let α1 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 α2 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 α3 be the total number 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 α4 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 M1 and G1 are NOT in the committee together.
| List - I | List - II |
| (P) The value of α1 is | (1) 136 |
| (Q) The value of α2 is | (2) 189 |
| (R) The value of α3 is | (3) 192 |
| (S) The value of α4 is | (4) 200 |
| (5) 381 | |
| (6) 461 |
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(P) α1 = 6C3 × 5C2 = 200
(1B and 1G) + (2B and 2G) + (3B and 3G) + (4B and 4G) + (5B and 5G)
(Q) α2 = 6C1 × 5C1 + 6C2 × 5C2 + 6C3 × 5C3 + 6C4 × 5C4 + 6C5 × 5C5
= 30 + 150 + 200 + 75 + 6
= 461
(R) α3 = 11C5 – (6C4 × 5C1 + 6C5) = 381
(S) α4 = 5C2 × 6C2 + 5C3 × 6C4 + 5C4 – (4C2 + 4C1 × 5C1)
= 150 + 60 + 5 – (6 + 20) = 189.