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Permutations and Combinations Calculations

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12 students are split 5 in room A, 4 in room B, and 3 in room C. How many different ways can this happen.

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Number of ways we can choose 5 students out of 12 = 12C5 = 792
<br>Now since 5 students have already been allocated to room A, we want to ...

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Permutation or Combination Calculations

For each question determine if the situation is a permutation or combination and if it is with or without replacement, then determine the answer.

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.

5 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?

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