Combinations and Probability

Question

A panel of 5 members is drawn from a group consisting of 2 managers, 7 assistants and 4 secretaries.

(a) How many ways can the panel be formed with at least 1 manager and 2 assistants

(b) Find the probability that the panel include 2 managers, 2 assistants and 1 secretary

(Bow)

Answer

(a) Should I use the following approach?

1M+2A+2S: C(2,1)*C(7,2)*C(4,2)=252

1M+3A+1S: C(2,1)*C(7,3)*C(4,1)=280

1M+4A+0S: C(2,1)*C(7,4)=70

2M+2A+1S: C(2,2)*C(7,2)*C(4,1)=84

2M+3A+0S: C(2,2)*C(7,3)=35

By addition, there are __721__ combinations.

(b) P=2/13*1/12*7/11*6/10*4/9=__14/6435__