Question

1. Consider sets AA and BB with |A|=9|| and |B|=19..

How many functions f:A→B are there?

Note: Leave your answer in exponential form. (Ex: 5^7)

2. Consider functions f:{1,2,3}→{1,2,3,4,5,6}.

How many functions between this domain and codomain are injective?

3. A combination lock consists of a dial with 39 numbers on it. To open the lock, you turn the dial to the right until you reach the first number, then to the left until you get to the second number, then to the right again to the third number. The numbers must be distinct. How many different combinations are possible? (Hint: Don't get fooled by the use of the word combination here!)

Answer 1