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Combinations and Permutations

1) Identify each of the following 1) as a permutation or combination and 2) as with or without replacement:

a) Social security numbers

b) Books in your backpack

c) Numbers chosen for the "Big" lotto

d) The cards in your hand for a card game

e) Lunch chosen by a student from the cafeteria menu

2) A cafeteria offers 4 main menu selections, 5 salad selections, 3 fruit selections and 8 drink selections. How many ways can a student choose a lunch if...

f) The student chooses one of each of the selections?

g) The student chooses two different main menu selections (must be different) and one salad?

h) The student chooses 3 salads (different), and a fruit?

i) The student chooses 4 salads (must be different), and a fruit?

j) The student chooses 5 items (main, salad or fruit), all different, and a drink?

k) The student chooses 2 different main menu items, 2 different salads, 2 pieces of different fruits and 1 drink (he plays football and is hungry!)

l) Which of these are combinations and which are permutations? Which are with and which without replacement?

Solution Preview

1) Identify each of the following 1) as a permutation or combination and 2) as with or without replacement:

a) Social security numbers

Combination with replacement:

If you think of SSN's as combinations of the numbers 0 - 9, then there is replacement, because a number can appear more than once in any given SSN.

b) Books in your backpack

Combination or permutation without replacement.

It depends on how you think of this. If the scenario is that you have a given number of books in your bag and you want to see how many ways you can pull them out, this would be a permutation. On the other hand, you had a large number of books in your ...

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