What is an example of a counting problem that can be solved with lists and another that can be solved with sets, how do I solve both problems?

Answer 1

Not sure what you mean by lists....

Here is a list

item # of cans per box

peaches 24

pears 30

pineapple 20

applesauce 12

If you have 10 boxes of peaches, 5 boxes of pears, 7 boxes of pineapples, and 8 boxes of applesauce,

how many cans are there in total?

Answer: 10*24 + 5*30 + 7*20 + 8*12 = 240 + 150 + 140 + 96 = 626

Perhaps you meant a problem that is solved USING lists....

Flipping 3 coins, how many combinations contain exactly 2 heads?

Here's the list:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

3 of them out of 8 contain exactly 2 heads, so the probability is 3/8 = 0.375 = 37.5%

Using sets?

Set X = { alpha, beta, delta}

How many possible subsets are there? How many contain delta?

there are 2^3 possible subsets.

empty set,

{alpha},

{beta},

{delta},

{alpha, beta}.

{alpha,delta}

{beta,delta}

{alpha,beta,delta}

4 contain delta