Respuesta :
According to the combination technique,
A) 3 from A and 1 from B = 16320
B) 2 from A and 2 from B = 29070
C) All from A = 3060
D) 4 people regardless of department = 73815
E) at least 3 from department A = 19380
In math combination technique is used to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Here we have given that 4-person grievance committee is to be selected out of 2 how many ways can the following committees be selected
And we need to find the following
Here we know that 4-person grievance committee is to be selected out of 2 departments, A and B, with 18 and 20 people.
In this one we have to find the number ways can the following committees be selected.
A) While the first condition is to 3 from A and 1 from B
Here the term "and" means to multiply
Then it can be written as
=> (18 people choose 3) x (20 people choose 1)
=> (18C3)(20C1) = (816)(20) = 16320
B) And then the next condition is 2 from A and 2 from B
In this one is written as,
=> (18 people choose 2) x (20 people choose 2)
=> (18C2)(20C2) = (153)(190) = 29070
C) All from A
which is equal to the following,
=> 18 people choose 4 = 18C4 = 3060
D) Next, we have to do the calculation for 4 people regardless of department
=> 18+20 or 38 people choose 4 = 38C4 = 73815
E) Finally, at least 3 from department A.
'In other words, it can be written as choose 3 from department A and choose 1 from department B or Choose 4 all from department A
Where "And" means to multiply and "or" means to add.
Therefore, the condition is written as,
=> [(18 people choose 3) times (20 people choose 1)] plus (18 people choose 4)
=> (18C3)(20C1) + (18C4) = (816)(20) + 3060 = 19380
To know more about Combination technique here.
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