Question 837998: Hello, My name is Sheila, and I would really like your help in solving this problem, and how to set it up.
The problem is a follow: How many one-to-one correspondence are there between the sets { x,y,z,u,v ] and {1,2,3,4,5 } if in each correspondence:
A. x must correspond to 5
B. x must correspond to 5 and y to 1
C. x,y,z must correspond to odd numbers
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
{ x,y,z,u,v ] and {1,2,3,4,5 }
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A. x must correspond to 5
{(x,5),(y,_),(z,_),(u,_),(v,_)}
We can choose
y's 2nd coordinate 4 ways,
z's 2nd coordinate 3 ways,
u's 2nd coordinate 2 ways,
v's 2nd coordinate 1 way.
Answer: 4·3·2·1 = 4! = 24 ways
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B. x must correspond to 5 and y to 1
{(x,5),(y,1),(z,_),(u,_),(v,_)}
We can choose
z's 2nd coordinate 3 ways,
u's 2nd coordinate 2 ways,
v's 2nd coordinate 1 way.
Answer: 3·2·1 = 3! = 6 ways
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C. x,y,z must correspond to odd numbers
{(x,_),(y,_),(z,_),(u,_),(v,_)}
We can choose
x's 2nd coordinate 3 ways, (1, 3 or 5)
y's 2nd coordinate 2 ways,
z's 2nd coordinate 1 way.
u's 2nd coordinate 2 ways, (2 or 4)
v's 2nd coordinate 1 way.
Answer: 3·2·1·2·1 = 3!2! = 6·2 = 12 ways
Edwin
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