Math 110T Socks Exercise

Math 110T Socks Exercise

Name______

In the exercises below, the exact number of the answer is not so important. What is important is the formula you use to figure out the answer. Indicate the formula (with specific numbers) that you would use.

Suppose you have twenty socks.

1.)  How many ways of choosing two socks out of the twenty are there?

2.)  How many ways of selecting ten socks from the twenty are there?

3.)  Suppose you put ten of the socks in one pile (call it “Pile A”) and the other ten socks in a second pile (call it “Pile B”). If you want to compare each sock in Pile A with each sock in Pile B, how many comparisons do you have to make?

4.)  If you want to put all twenty socks in a row, how many ways of doing this are there?

5.)  If you want to pick out ten of the socks and then put them in a row, how many ways of doing this are there?

6.)  Let’s say you just washed all your socks and you want to sort them into matching pairs. Assume that each sock only matches one other sock. Here’s a procedure you might use:

a)  Make two piles of socks (“Pile A and Pile B”) each pile having ten socks.

b)  Take a sock from Pile B and compare it with the first sock from Pile A. If it matches, put the two socks in a new pile (“Pile C”) otherwise put the sock you took from Pile B in Pile D.

c)  Take another sock from Pile B and do the same thing you did in Step b).

d)  Repeat Step c) until there are no more socks in Pile B.

e)  Divide Pile D into two piles and go through Steps b to d with it.

f)  Divide Pile A into two piles and go through Steps b to d with it.

Now, your job is to diagram out this somewhat complicated procedure. To do this, make a directed graph where the vertices (the nodes) are labeled with the operations you have to do and the edges connect each operation to the operation(s) you do next. You can be flexible with this if you need to (that is, you can be a little creative here if you need to be).