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Permutation

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
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3 Solutions

Commented:
this sounds like you want combinations not permutations

C(n,r) = n!/(r!(n-r!))
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Author Commented:
How to know that its a combination or permutation ?
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Commented:

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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Author Commented:
so according to the question part a is about permutation right?
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Commented:
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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Commented:
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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Commented:
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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Author Commented:
what are the 2 formulas for permutation and combination
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Commented:
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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Author 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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Commented:
does the order of the people in the group matter or not?
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Author Commented:
No
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Commented:
if order makes a difference, its a permutation.  If order makes no difference, its a combination
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Commented:
if the order doesn't matter, then it's a combination.

C(n,r) = n!/(r!(n-r)!)  = 210
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Commented:
I don't understand the split.