Question

Out of 10 students there are 6 girls and 4 boys.A team of 4 students is selected at random.Find the probability that there are at least 2 girls.

Answer 1

The total ways in which selection can be made =10C4
=210 ways
The required selection of having at least 2 girls can be
1.2 girls and 2 boys =(6C2 ×4C2)
2.3 girls and 1 boy=(6C3×4C1)
3.4 girls =6C4
so total number of selection =(6C2×4C2)+(6C3×4C1)+6C4
=90+80+15
=185
So P(at least 2 girls)=185/
​​​​​​210
=37/42
​​​