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Hugo and Viviana work in an office with eight other co-workers. Out of these 10 workers, their boss needs to choose a group of four to work together on a project.

a. How many different working groups of four can the boss choose?
b. Suppose Hugo and Viviana absolutely refuse, under any circumstances, to work together. Under this restriction, how many different working groups of four can be formed ?
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Is this is correct
a. P(n,r)=n!/(n-r)!
P(10,2)=10!/(10-2)!
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mustish1
Asked:
mustish1
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3 Solutions
 
sdstuberCommented:
this sounds like you want combinations not permutations


C(n,r) = n!/(r!(n-r!))
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mustish1Author Commented:
How to know that its a combination or permutation ?
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sdstuberCommented:
as in your previous question


permutation distinguishes different orderings
combination does not

Scott, Tom, Sally, Sue   is the same group as Sally, Tom, Sue, Scott  

right?

if so, that's a combination

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mustish1Author Commented:
so according to the question part a is about permutation right?
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ozoCommented:
permutation would mean that Scott, Tom, Sally, Sue  is a different group from Sally, Tom, Sue, Scott  
Does the boss distinguish those groups?
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sdstuberCommented:
you tell me.

if the boss picks Scott, Tom, Sally, Sue  for a group.

is that different than if he picks   Sally, Tom, Sue, Scott?

it's the same 4 people.  I simply listed them in different order.
Does that matter?

if it does, then you want permutations
if it does not, then you want combinations
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sdstuberCommented:
assuming you do want combinations

then for part B

C(8,4) + C(8,3) + C(8,3)  = 182

C(8,4) =  all combinations of 4 employees that don't include either Hugo or Viviana

C(8,3) = all combinations of 3 employees that could partner with Hugo  (except Viviana)

C(8,3) = all combinations of 3 employees that could partner with Viviana (except Hugo)
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mustish1Author Commented:
what are the 2 formulas for permutation and combination
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sdstuberCommented:
combination:
    C(n,r) = n!/(r!(n-r)!)       --- sorry I had a typo and misplaced a factorial (!) in my first post

permutation:

   P(n,r) = n!/(n-r)!
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mustish1Author Commented:
ok thanks. Can you please tell me the part a its a permutation or combination

a. How many different working groups of four can the boss choose?
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ozoCommented:
does the order of the people in the group matter or not?
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mustish1Author Commented:
No
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ozoCommented:
if order makes a difference, its a permutation.  If order makes no difference, its a combination
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sdstuberCommented:
if the order doesn't matter, then it's a combination.


C(n,r) = n!/(r!(n-r)!)  = 210
part b is already posted
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sdstuberCommented:
I don't understand the split.

how is  http:#37033589  an answer?

first, it's just a question

second,  it's a repeat question of http:#37033507 
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