Stat 400, chapter 2, Probability, Permutations and Combinations
supplemental handout prepared by Tim Pilachowski
An arrangement in which the order of objects or events makes a difference, e.g. RYB ≠ RBY, is called a
permutation. When the order of objects or events does not make a difference, e.g. RYB = RBY = BYR, etc, we
have a combination.
Answer the questions in the Examples below first yourself, first. Only look at the worked-out answers after
you’ve tried them for yourself.
Example A. a) In Arithmetic, addition is both commutative and associative, that is numbers can be rearranged
and regrouped in any way and the answer will still be the same. Is addition more like a combination or
permutation? b) In Arithmetic, division is neither commutative nor associative. It makes a difference whether
one is calculating “p divided by q” or “q divided by p”. Is division more like a combination or permutation?
Example B. a) The cook at Pappy’s Restaurant makes a pizza by first rolling out and stretching the dough for
the crust, then spreading out the sauce, then adding cheese and toppings. Is making a pizza more like a
combination or permutation? b) The cook at Bel-Loc Diner makes sausage stew by throwing all of the
ingredients into a pot and letting it simmer for four hours. Is making stew more like a combination or
permutation?
Example C. a) Harold Hill puts his knick knacks on a shelf according to whatever whim hits him at the moment,
and is likely to move them around periodically. Is Harold’s method an example of a combination or
permutation? b) Marian puts books on the shelf in the town’s library, arranging them by using their call
numbers. Is Marian’s method an example of a combination or permutation?
Example D. In the Maryland Lottery’s Pick 4 game, players have a choice of the type of bet. “Straight – Your
number must match the winning number in exact order. Box – Your number can match the winning number in
any order.” (source: mdlottery.com) a) Is playing “Straight” an example of a combination or permutation? b) Is
playing “Box” an example of a combination or permutation?
Example E. a) Twenty runners stand on the starting line at the beginning of a marathon. Is this an example of a
combination or a permutation? b) Ribbons are awarded to first-, second-, and third-place finishers. Is this an
example of a combination or a permutation?
Example F. A combination lock requires the user to know a set of three one-digit numbers which must be
entered in a particular way. For example, if the correct combination is “1-3-5”, then entering “5-1-3” or “3-5-1”
won’t open the lock. Is a “combination lock” an example of a combination or a permutation?
Example G. In a game of bridge, using a standard deck of fifty-two playing cards, each of four players is dealt
thirteen cards. Is this an example of a combination or permutation? How many possible bridge hands are there?
