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Permutations and Combinations question

2018 · Shift 2 · Q34
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  5. /2018 · Shift 2 · Q34

Permutations and Combinations question

2018 · Shift 2 · Q34

JEE AdvancedMathematicsPermutations and CombinationsMCQ+3 / −1
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 α\alphaα1 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\alphaα2 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.

i) Let α\alphaα3 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 α\alphaα4 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 such that both M1 and G1 are NOT in the committee together.
LIST-I LIST-II
P. The value of α1\alpha_1α1​ is 1. 136
Q. The value of α2\alpha_2α2​ is 2. 189
R. The value of α3\alpha_3α3​ is 3. 192
S. The value of α4\alpha_4α4​ is 4. 200
5. 381
6. 461
The correct option is
  1. A
    P →\to→ 4; Q →\to→ 6; R →\to→ 2; S →\to→ 1
  2. B
    P →\to→ 1; Q →\to→ 4; R →\to→ 2; S →\to→ 3
  3. C
    P →\to→ 4; Q →\to→ 6; R →\to→ 5; S →\to→ 2
  4. D
    P →\to→ 4; Q →\to→ 2; R →\to→ 3; S →\to→ 1
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