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
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