2. Let set A have 4 elements and set B have 5 elements. How many functions are t

Question

2. Let set A have 4 elements and set B have 5 elements. How many functions are there from set A to set B? How many one-to-one functions are there from set A to set B? And how many one-to-one functions are there from set B to set A? Give explanation for each of your answers.

3. Suppose that there were 100 million wage eamers in US last year who eamed less than 1 million dollars. Prove that there were two of them who eamed exactly the same amount of money, to the penny, last year.

4. A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women altemate? Give explanation for your answer.

Explanation / Answer

1) 4 one to one and 4 onto

2) as the 100 million wage earners are there, if we consider one to one function then the earn must be equal to 1 million each, but in our case it fails

so this is onto function, where every element must map to set b elements, where atleast two elements must have common. So,  there were two of them who eamed exactly the same amount of money, to the penny, last year.

3)

The number of ways to arrange the men in order is n! Likewise for the number of women. So if you don't care whether a man or woman starts the row, the answer would (n!)2, since you need to consider each possible permutation of men with any possible permutation of women. Since you do, multiply by 2.

so, The correct answer is 2(n!)^2

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