10.4 fundamental counting priciple and permutations

10.4 counting and perumtations.notebook March 27, 2013

How many lunch specials can you choose from if you can choose chicken, pasta or fish as a main dish and soup or salad as a side dish?

Fundamental Counting Principle:

Two Events Three Eventsm n m n p


You are ordering a case for your MP3 player. You can choose any of 30 colorsfor the main shell, and of 32 colors for the protective band, and any of 200 decals for the cover screen. How many different cases are possible?


You are choosing a password that has 4 letters followed by 2 digits.

How many passwords are possible if the letters and digits can be repeated?

How many passwords are possible if the letters and digits cannot be repeated?


Permutations an ordering of a set of objects

There are 6 permutations of the Letters A, B, and C

ABC ACB BAC BCA CAB CBA

By the counting principle: ___ ___ ___

The number of permutations of n distinct objects is n!.

Examples

4! 5! 6!


Eight skiers are competing in a moguls (snow bumps) competition.

In how many different orders can the skiers finish the competition?

In how many different ways can 3 of the skiers finish first through third?


In the second question above, an ordered group of 3 skiers is taken from the group of 8 skiers.This is a permutation of 8 objects taken 3 at a time. It is denoted by 8P3. Or . . .

8P3 =

The number of permutations of n objects taken r at a time is denoted by nPr = n!(n r)!


You have 6 text messages on your cell phone. In how many orders can you reply to 4 of the messages? to all 6?

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10.4 fundamental counting priciple and permutations