1. ## [SOLVED] Functions

How many functions are there from {0,1,...,n-1} to {0,1} where n > 1 that:
1)are one to one
2)assign 0 to both 0 and n-1.
3)assign 1 to exactly one positive integer less than n-1.

Here is what ive done:

1) n C 2 = x, and since you can arrange it in 2 ways, then 2x.
For e.g: 2 C 2 = 1, 1 x 2 = 2 one -to-one functions.

2)Im not sure. Would like some help. There will be at least 1 function
(0 - 0). But confused about n-1!

3) im not sure what its asking, im confused. Taking a guess ill say it is
n-1 C 1.

Can i please have some help on 2 and 3 please and a check if im correct on Q1.

2. Originally Posted by kurac
How many functions are there from {0,1,...,n-1} to {0,1} where n > 1 that:
1)are one to one
2)assign 0 to both 0 and n-1.
3)assign 1 to exactly one positive integer less than n-1.
3) $n-2$ if $n\ge3$.