JEE Advanced2018MathematicsPermutation and CombinationActual
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 leas
Options
- Aa-s;b-u;c-t;d-q;
- Ba-u;b-t;c-q;d-p;
- Ca-t;b-r;c-s;d-p;
- Da-t;b-r;c-q;d-p;
Correct answer
A. a-s;b-u;c-t;d-q;
Step-by-step solution
1 α 1 = 6 3 5 2 = 200 So P → 4 2 α 2 = 6 1 5 1 + 6 2 5 2 + 6 3 2 3 + 6 4 5 4 + 6 5 5 5 = 11 5 - 1 = 461 So Q → 6 3 α 3 = 5 2 6 3 + 5 3 6 2 + 5 4 6 1 + 5 5 6 0 = 11 5 - 5 0 6 5 - 5 1 6 4 = 381 So R → 5 4 α 2 = 5 2 6 2 - 4 1 5 1 + 5 3 6 1 - 4 2 1 1 + 5 4 = 189 So S → 2