SOLUTION: A 4-person grievance committee is to be selected out of 2 departments, A and B, with 18 and 20 people. In how many ways can the following committees be selected. A) 3 from A

Algebra ->  Permutations -> SOLUTION: A 4-person grievance committee is to be selected out of 2 departments, A and B, with 18 and 20 people. In how many ways can the following committees be selected. A) 3 from A      Log On


   

Question 1031373: A 4-person grievance committee is to be selected out of 2
departments, A and B, with 18 and 20 people. In how many
ways can the following committees be selected.
A) 3 from A and 1 from B
B) 2 from A and 2 from B
C) All from A
D) 4 people regardless of department
E) at least 3 from department A.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A 4-person grievance committee is to be selected out of 2
departments, A and B, with 18 and 20 people. In how many
ways can the following committees be selected.
A) 3 from A and 1 from B 

"and" means to multiply

So that's (18 people choose 3) times (20 people choose 1) =
(18C3)(20C1) = (816)(20) = 16320

B) 2 from A and 2 from B 
"and" means to multiply

So that's (18 people choose 2) times (20 people choose 2) =
(18C2)(20C2) = (153)(190) = 29070

C) All from A 
That's 18 people choose 4 = 18C4 = 3060

D) 4 people regardless of department
That's 18+20 or 38 people choose 4 = 38C4 = 73815

E) at least 3 from department A.
Choose 3 from department A and choose 1 from department B  

or

Choose 4 all from department A

"And" means to multiply and "or" means to add.

That's

[(18 people choose 3) times (20 people choose 1)] plus 
(18 people choose 4) =

(18C3)(20C1) + (18C4) = (816)(20) + 3060 = 19380

Edwin