13. Consider functions f: {1,2,3,4} {1, 2, 3, 4, 5, 6}. → a. How many functions are there total? b. How many functions are injective? c. How many of the injective functions are increasing? To be increasing means that if a < b then f(a) f(b), or in other words, the outputs get larger as the inputs get larger. 14. We have seen that the formula for P(n, k) is n! (n-k)! Your task here is to explain why this is the right formula. a. Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make? Explain your answer and why it is the same as using the formula for P(12,5). b. Using the scenario of the 12 chips again, what does 12! count? What does 7! count? Explain. c. Explain why it makes sense to divide 12! by 7! when computing P(12,5) (in terms of the chips). d. Does your explanation work for numbers other than 12 and 5? Explain the formula P(n, k) = using the variables n and k. n! (n-k)!