Total number of different committees = C(14,6) = N
We have two cases where we have less than 2 teachers.
case 1: 1 teacher (out of 5)
Number of ways to choose 1 teacher = C(5,1) = 5
Number of ways to choose the remaining members from students = C(9,5)
Total number of ways to choose a committee with exactly 1 teacher = 5C(9,5) = N1
case 2: no teacher
Number of ways to choose 6 students = C(9,6) = N2 Probability to choose at least two teachers
= (N-N1-N2)/N
=109/143
I hope tmy answer helps you
