A company has 22 staff members - the owner, 3 senior executives, 14 junior executives and 4 support staff. A committee of 8 members of the staff must be convened and the members are selected at random.
a) what is the probability that there are fewer support staff on the committee than senior executives.
b) what is the probability that the owner in on the committee and there is at least one member from each of the 3 staff categories on the committee too?

Question

A company has 22 staff members - the owner, 3 senior executives, 14 junior executives and 4 support staff. A committee of 8 members of the staff must be convened and the members are selected at random.
a) what is the probability that there are fewer support staff on the committee than senior executives.
b) what is the probability that the owner in on the committee and there is at least one member from each of the 3 staff categories  on the committee too?