SOLUTION: Count the number X of functions φ:(46,47,...,49)→(25,26,...,28) so that φ is not onto. X

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Question 930372: Count the number X of functions
φ:(46,47,...,49)→(25,26,...,28)
so that φ is not onto.
X
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The total number of functions is 4^4 = 256. The number of onto functions turns out to be 4! = 24 since the domain and range both have size 4, and assuming 45, 46, 47, 48 are mapped, the function must be bijective. Then the number of functions that are not onto is 256-24 = 232.